[{"day":"01","doi":"10.1090/conm/412","intvolume":" 412","date_created":"2018-12-11T11:57:03Z","quality_controlled":0,"year":"2006","conference":{"name":"Differential Equations and Mathematical Physics"},"date_published":"2006-01-01T00:00:00Z","publisher":"American Mathematical Society","month":"01","_id":"2333","type":"conference","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0507049","open_access":"1"}],"title":"Ground-state energy of a dilute Fermi gas","citation":{"short":"É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006, pp. 239–248.","ama":"Lieb É, Seiringer R, Solovej J. Ground-state energy of a dilute Fermi gas. In: Vol 412. American Mathematical Society; 2006:239-248. doi:10.1090/conm/412","ista":"Lieb É, Seiringer R, Solovej J. 2006. Ground-state energy of a dilute Fermi gas. Differential Equations and Mathematical Physics, Contemporary Mathematics, vol. 412, 239–248.","apa":"Lieb, É., Seiringer, R., & Solovej, J. (2006). Ground-state energy of a dilute Fermi gas (Vol. 412, pp. 239–248). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/412","mla":"Lieb, Élliott, et al. *Ground-State Energy of a Dilute Fermi Gas*. Vol. 412, American Mathematical Society, 2006, pp. 239–48, doi:10.1090/conm/412.","ieee":"É. Lieb, R. Seiringer, and J. Solovej, “Ground-state energy of a dilute Fermi gas,” presented at the Differential Equations and Mathematical Physics, 2006, vol. 412, pp. 239–248.","chicago":"Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground-State Energy of a Dilute Fermi Gas,” 412:239–48. American Mathematical Society, 2006. https://doi.org/10.1090/conm/412."},"extern":1,"volume":412,"page":"239 - 248","publist_id":"4593","status":"public","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"}],"publication_status":"published","alternative_title":["Contemporary Mathematics"],"oa":1,"date_updated":"2021-01-12T06:56:51Z"},{"date_updated":"2021-01-12T06:56:51Z","oa":1,"editor":[{"first_name":"Jean","last_name":"Zambrini","full_name":"Zambrini, Jean-Claude"}],"publist_id":"4592","status":"public","author":[{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"publication_status":"published","_id":"2334","type":"conference","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0305025"}],"title":"One-dimensional behavior of dilute, trapped Bose gases in traps","citation":{"chicago":"Seiringer, Robert, Élliott Lieb, and Jakob Yngvason. “One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps.” edited by Jean Zambrini. World Scientific Publishing, 2006. https://doi.org/10.1007/s00220-003-0993-3.","ieee":"R. Seiringer, É. Lieb, and J. Yngvason, “One-dimensional behavior of dilute, trapped Bose gases in traps,” presented at the ICMP: International Congress on Mathematical Physics, 2006.","ista":"Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute, trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics.","mla":"Seiringer, Robert, et al. *One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps*. Edited by Jean Zambrini, World Scientific Publishing, 2006, doi:10.1007/s00220-003-0993-3.","apa":"Seiringer, R., Lieb, É., & Yngvason, J. (2006). One-dimensional behavior of dilute, trapped Bose gases in traps. In J. Zambrini (Ed.). Presented at the ICMP: International Congress on Mathematical Physics, World Scientific Publishing. https://doi.org/10.1007/s00220-003-0993-3","ama":"Seiringer R, Lieb É, Yngvason J. One-dimensional behavior of dilute, trapped Bose gases in traps. In: Zambrini J, ed. World Scientific Publishing; 2006. doi:10.1007/s00220-003-0993-3","short":"R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific Publishing, 2006."},"extern":1,"date_published":"2006-03-07T00:00:00Z","publisher":"World Scientific Publishing","month":"03","date_created":"2018-12-11T11:57:03Z","conference":{"name":"ICMP: International Congress on Mathematical Physics"},"quality_controlled":0,"year":"2006","day":"07","doi":"10.1007/s00220-003-0993-3"},{"issue":"2","date_updated":"2020-07-14T12:45:40Z","oa":1,"publication_status":"published","author":[{"full_name":"Lieb, Élliott H","last_name":"Lieb","first_name":"Élliott"},{"last_name":"Seiringer","full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"status":"public","publist_id":"4561","page":"505 - 537","volume":264,"extern":1,"citation":{"short":"É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006) 505–537.","ama":"Lieb É, Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. 2006;264(2):505-537. doi:10.1007/s00220-006-1524-9","mla":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*, vol. 264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9.","apa":"Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-006-1524-9","ista":"Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.","ieee":"É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for rotating Bose gases,” *Communications in Mathematical Physics*, vol. 264, no. 2. Springer, pp. 505–537, 2006.","chicago":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9."},"abstract":[{"lang":"eng","text":" We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. "}],"publication":"Communications in Mathematical Physics","title":"Derivation of the Gross-Pitaevskii equation for rotating Bose gases","_id":"2363","type":"review","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0504042","open_access":"1"}],"month":"01","publisher":"Springer","date_published":"2006-01-01T00:00:00Z","quality_controlled":0,"year":"2006","date_created":"2018-12-11T11:57:13Z","intvolume":" 264","doi":"10.1007/s00220-006-1524-9","day":"01"},{"oa":1,"date_updated":"2021-01-12T06:57:02Z","issue":"3","page":"233 - 253","volume":18,"author":[{"full_name":"Robert Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"publication_status":"published","status":"public","publist_id":"4562","publisher":"World Scientific Publishing","date_published":"2006-04-01T00:00:00Z","month":"04","title":"A correlation estimate for quantum many-body systems at positive temperature","publication":"Reviews in Mathematical Physics","_id":"2364","type":"journal_article","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0601051","open_access":"1"}],"extern":1,"abstract":[{"lang":"eng","text":"We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation."}],"citation":{"chicago":"Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2006. https://doi.org/10.1142/S0129055X06002632.","ieee":"R. Seiringer, “A correlation estimate for quantum many-body systems at positive temperature,” *Reviews in Mathematical Physics*, vol. 18, no. 3. World Scientific Publishing, pp. 233–253, 2006.","ista":"Seiringer R. 2006. A correlation estimate for quantum many-body systems at positive temperature. Reviews in Mathematical Physics. 18(3), 233–253.","apa":"Seiringer, R. (2006). A correlation estimate for quantum many-body systems at positive temperature. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X06002632","mla":"Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” *Reviews in Mathematical Physics*, vol. 18, no. 3, World Scientific Publishing, 2006, pp. 233–53, doi:10.1142/S0129055X06002632.","short":"R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253.","ama":"Seiringer R. A correlation estimate for quantum many-body systems at positive temperature. *Reviews in Mathematical Physics*. 2006;18(3):233-253. doi:10.1142/S0129055X06002632"},"intvolume":" 18","doi":"10.1142/S0129055X06002632","day":"01","quality_controlled":0,"year":"2006","date_created":"2018-12-11T11:57:14Z"},{"oa":1,"issue":"3","date_updated":"2021-01-12T06:57:02Z","status":"public","publist_id":"4563","publication_status":"published","author":[{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer"}],"volume":261,"page":"729 - 757","month":"02","date_published":"2006-02-01T00:00:00Z","publisher":"Springer","citation":{"short":"R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.","ama":"Seiringer R. The thermodynamic pressure of a dilute fermi gas. *Communications in Mathematical Physics*. 2006;261(3):729-757. doi:10.1007/s00220-005-1433-3","ista":"Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications in Mathematical Physics. 261(3), 729–757.","apa":"Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-005-1433-3","mla":"Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications in Mathematical Physics*, vol. 261, no. 3, Springer, 2006, pp. 729–57, doi:10.1007/s00220-005-1433-3.","chicago":"Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s00220-005-1433-3.","ieee":"R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” *Communications in Mathematical Physics*, vol. 261, no. 3. Springer, pp. 729–757, 2006."},"abstract":[{"lang":"eng","text":"We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller."}],"extern":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0412086"}],"_id":"2365","type":"journal_article","title":"The thermodynamic pressure of a dilute fermi gas","publication":"Communications in Mathematical Physics","day":"01","doi":"10.1007/s00220-005-1433-3","intvolume":" 261","date_created":"2018-12-11T11:57:14Z","quality_controlled":0,"year":"2006"},{"title":"Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials","publication":"Letters in Mathematical Physics","_id":"2366","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0605017"}],"type":"journal_article","extern":1,"abstract":[{"text":"Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.","lang":"eng"}],"citation":{"short":"R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics 77 (2006) 309–316.","ama":"Frank R, Laptev A, Lieb É, Seiringer R. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. *Letters in Mathematical Physics*. 2006;77(3):309-316. doi:10.1007/s11005-006-0095-1","apa":"Frank, R., Laptev, A., Lieb, É., & Seiringer, R. (2006). Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-006-0095-1","mla":"Frank, Rupert, et al. “Lieb-Thirring Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters in Mathematical Physics*, vol. 77, no. 3, Springer, 2006, pp. 309–16, doi:10.1007/s11005-006-0095-1.","ista":"Frank R, Laptev A, Lieb É, Seiringer R. 2006. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Letters in Mathematical Physics. 77(3), 309–316.","ieee":"R. Frank, A. Laptev, É. Lieb, and R. Seiringer, “Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials,” *Letters in Mathematical Physics*, vol. 77, no. 3. Springer, pp. 309–316, 2006.","chicago":"Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s11005-006-0095-1."},"publisher":"Springer","date_published":"2006-09-01T00:00:00Z","month":"09","quality_controlled":0,"year":"2006","date_created":"2018-12-11T11:57:15Z","doi":"10.1007/s11005-006-0095-1","intvolume":" 77","day":"01","date_updated":"2021-01-12T06:57:03Z","issue":"3","oa":1,"page":"309 - 316","volume":77,"author":[{"first_name":"Rupert","full_name":"Frank, Rupert L","last_name":"Frank"},{"full_name":"Laptev, Ari","last_name":"Laptev","first_name":"Ari"},{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"publication_status":"published","publist_id":"4560","status":"public"},{"date_updated":"2021-01-12T06:57:03Z","editor":[{"first_name":"Jan","full_name":"Dereziński, Jan","last_name":"Dereziński"},{"first_name":"Heinz","full_name":"Siedentop, Heinz","last_name":"Siedentop"}],"alternative_title":["LNP"],"volume":695,"page":"249 - 274","publist_id":"4558","status":"public","publication_status":"published","author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"_id":"2368","type":"book_chapter","title":"Dilute, trapped Bose gases and Bose-Einstein condensation","publication":"Large Coulomb Systems","citation":{"ista":"Seiringer R. 2006.Dilute, trapped Bose gases and Bose-Einstein condensation. In: Large Coulomb Systems. LNP, vol. 695, 249–274.","mla":"Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.” *Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop, vol. 695, Springer, 2006, pp. 249–74, doi:10.1007/3-540-32579-4_6.","apa":"Seiringer, R. (2006). Dilute, trapped Bose gases and Bose-Einstein condensation. In J. Dereziński & H. Siedentop (Eds.), *Large Coulomb Systems* (Vol. 695, pp. 249–274). Springer. https://doi.org/10.1007/3-540-32579-4_6","short":"R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems, Springer, 2006, pp. 249–274.","ama":"Seiringer R. Dilute, trapped Bose gases and Bose-Einstein condensation. In: Dereziński J, Siedentop H, eds. *Large Coulomb Systems*. Vol 695. Springer; 2006:249-274. doi:10.1007/3-540-32579-4_6","ieee":"R. Seiringer, “Dilute, trapped Bose gases and Bose-Einstein condensation,” in *Large Coulomb Systems*, vol. 695, J. Dereziński and H. Siedentop, Eds. Springer, 2006, pp. 249–274.","chicago":"Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.” In *Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop, 695:249–74. Springer, 2006. https://doi.org/10.1007/3-540-32579-4_6."},"abstract":[{"lang":"eng","text":"The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases."}],"extern":1,"date_published":"2006-01-01T00:00:00Z","publisher":"Springer","month":"01","date_created":"2018-12-11T11:57:15Z","quality_controlled":0,"year":"2006","day":"01","intvolume":" 695","doi":"10.1007/3-540-32579-4_6"},{"doi":"10.1007/b11573432","intvolume":" 690","day":"01","year":"2006","quality_controlled":0,"date_created":"2018-12-11T11:57:16Z","publisher":"Springer","date_published":"2006-01-01T00:00:00Z","month":"01","publication":"Mathematical Physics of Quantum Mechanics","title":"Bose-Einstein condensation as a quantum phase transition in an optical lattice","main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0412034","open_access":"1"}],"_id":"2369","type":"book_chapter","extern":1,"citation":{"ama":"Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. Bose-Einstein condensation as a quantum phase transition in an optical lattice. In: Asch J, Joye A, eds. *Mathematical Physics of Quantum Mechanics*. Vol 690. Springer; 2006:199-215. doi:10.1007/b11573432","short":"M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, J. Asch, A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Springer, 2006, pp. 199–215.","mla":"Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.” *Mathematical Physics of Quantum Mechanics*, edited by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:10.1007/b11573432.","ista":"Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006.Bose-Einstein condensation as a quantum phase transition in an optical lattice. In: Mathematical Physics of Quantum Mechanics. LNP, vol. 690, 199–215.","apa":"Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2006). Bose-Einstein condensation as a quantum phase transition in an optical lattice. In J. Asch & A. Joye (Eds.), *Mathematical Physics of Quantum Mechanics* (Vol. 690, pp. 199–215). Springer. https://doi.org/10.1007/b11573432","ieee":"M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein condensation as a quantum phase transition in an optical lattice,” in *Mathematical Physics of Quantum Mechanics*, vol. 690, J. Asch and A. Joye, Eds. Springer, 2006, pp. 199–215.","chicago":"Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.” In *Mathematical Physics of Quantum Mechanics*, edited by Joachim Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432."},"abstract":[{"lang":"eng","text":"One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results."}],"page":"199 - 215","volume":690,"publication_status":"published","author":[{"full_name":"Aizenman, Michael","last_name":"Aizenman","first_name":"Michael"},{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert"},{"full_name":"Solovej, Jan P","last_name":"Solovej","first_name":"Jan"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"publist_id":"4559","status":"public","alternative_title":["LNP"],"oa":1,"editor":[{"first_name":"Joachim","full_name":"Asch, Joachim","last_name":"Asch"},{"first_name":"Alain","full_name":"Joye, Alain","last_name":"Joye"}],"date_updated":"2021-01-12T06:57:04Z"},{"alternative_title":["Algorithms and Combinatorics"],"publication_status":"published","author":[{"full_name":"Bang-Jensen, Jørgen","last_name":"Bang Jensen","first_name":"Jørgen"},{"last_name":"Reed","full_name":"Reed, Bruce","first_name":"Bruce"},{"first_name":"Bruce","last_name":"Schacht","full_name":"Schacht, Bruce"},{"first_name":"Robert","last_name":"Šámal","full_name":"Šámal, Robert"},{"full_name":"Toft, Bjarne","last_name":"Toft","first_name":"Bjarne"},{"full_name":"Uli Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"publist_id":"4509","status":"public","page":"613 - 627","volume":26,"date_updated":"2021-01-12T06:57:21Z","year":"2006","quality_controlled":0,"date_created":"2018-12-11T11:57:32Z","doi":"10.1007/3-540-33700-8_30","intvolume":" 26","day":"01","extern":1,"citation":{"mla":"Bang Jensen, Jørgen, et al. “On Six Problems Posed by Jarik Nešetřil.” *Topics in Discrete Mathematics*, vol. 26, Springer, 2006, pp. 613–27, doi:10.1007/3-540-33700-8_30.","ista":"Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. 2006.On six problems posed by Jarik Nešetřil. In: Topics in Discrete Mathematics. Algorithms and Combinatorics, vol. 26, 613–627.","apa":"Bang Jensen, J., Reed, B., Schacht, B., Šámal, R., Toft, B., & Wagner, U. (2006). On six problems posed by Jarik Nešetřil. In *Topics in Discrete Mathematics* (Vol. 26, pp. 613–627). Springer. https://doi.org/10.1007/3-540-33700-8_30","short":"J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, U. Wagner, in:, Topics in Discrete Mathematics, Springer, 2006, pp. 613–627.","ama":"Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. On six problems posed by Jarik Nešetřil. In: *Topics in Discrete Mathematics*. Vol 26. Springer; 2006:613-627. doi:10.1007/3-540-33700-8_30","ieee":"J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, and U. Wagner, “On six problems posed by Jarik Nešetřil,” in *Topics in Discrete Mathematics*, vol. 26, Springer, 2006, pp. 613–627.","chicago":"Bang Jensen, Jørgen, Bruce Reed, Bruce Schacht, Robert Šámal, Bjarne Toft, and Uli Wagner. “On Six Problems Posed by Jarik Nešetřil.” In *Topics in Discrete Mathematics*, 26:613–27. Springer, 2006. https://doi.org/10.1007/3-540-33700-8_30."},"publication":"Topics in Discrete Mathematics","title":"On six problems posed by Jarik Nešetřil","_id":"2416","type":"book_chapter","month":"01","publisher":"Springer","date_published":"2006-01-01T00:00:00Z"},{"publication_status":"published","author":[{"full_name":"Matoušek, Jiří","last_name":"Matoušek","first_name":"Jiří"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"last_name":"Smorodinsky","full_name":"Smorodinsky, Shakhar","first_name":"Shakhar"},{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","full_name":"Uli Wagner","last_name":"Wagner","first_name":"Uli","orcid":"0000-0002-1494-0568"}],"publist_id":"4495","status":"public","page":"177 - 191","volume":35,"issue":"2","date_updated":"2021-01-12T06:57:26Z","quality_controlled":0,"year":"2006","date_created":"2018-12-11T11:57:37Z","doi":"10.1007/s00454-005-1200-4","intvolume":" 35","day":"01","extern":1,"abstract":[{"lang":"eng","text":"We show, with an elementary proof, that the number of halving simplices in a set of n points in 4 in general position is O(n4-2/45). This improves the previous bound of O(n4-1/134). Our main new ingredient is a bound on the maximum number of halving simplices intersecting a fixed 2-plane. "}],"citation":{"chicago":"Matoušek, Jiří, Micha Sharir, Shakhar Smorodinsky, and Uli Wagner. “K-Sets in Four Dimensions.” *Discrete & Computational Geometry*. Springer, 2006. https://doi.org/10.1007/s00454-005-1200-4.","ieee":"J. Matoušek, M. Sharir, S. Smorodinsky, and U. Wagner, “K-sets in four dimensions,” *Discrete & Computational Geometry*, vol. 35, no. 2. Springer, pp. 177–191, 2006.","ista":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. 2006. K-sets in four dimensions. Discrete & Computational Geometry. 35(2), 177–191.","mla":"Matoušek, Jiří, et al. “K-Sets in Four Dimensions.” *Discrete & Computational Geometry*, vol. 35, no. 2, Springer, 2006, pp. 177–91, doi:10.1007/s00454-005-1200-4.","apa":"Matoušek, J., Sharir, M., Smorodinsky, S., & Wagner, U. (2006). K-sets in four dimensions. *Discrete & Computational Geometry*. Springer. https://doi.org/10.1007/s00454-005-1200-4","short":"J. Matoušek, M. Sharir, S. Smorodinsky, U. Wagner, Discrete & Computational Geometry 35 (2006) 177–191.","ama":"Matoušek J, Sharir M, Smorodinsky S, Wagner U. K-sets in four dimensions. *Discrete & Computational Geometry*. 2006;35(2):177-191. doi:10.1007/s00454-005-1200-4"},"title":"K-sets in four dimensions","publication":"Discrete & Computational Geometry","_id":"2429","type":"journal_article","month":"02","publisher":"Springer","date_published":"2006-02-01T00:00:00Z"}]