{"_id":"1156","title":"Facets of the r-stable (n, k)-hypersimplex","date_created":"2018-12-11T11:50:27Z","page":"815 - 829","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"quality_controlled":0,"day":"01","volume":20,"date_updated":"2021-01-12T06:48:43Z","abstract":[{"text":"Let k, n, and r be positive integers with k &lt; n and r≤⌊nk⌋. We determine the facets of the r-stable n, k-hypersimplex. As a result, it turns out that the r-stable n, k-hypersimplex has exactly 2n facets for every r&lt;⌊nk⌋. We then utilize the equations of the facets to study when the r-stable hypersimplex is Gorenstein. For every k &gt; 0 we identify an infinite collection of Gorenstein r-stable hypersimplices, consequently expanding the collection of r-stable hypersimplices known to have unimodal Ehrhart δ-vectors.","lang":"eng"}],"publication":"Annals of Combinatorics","intvolume":"        20","publisher":"Springer","doi":"10.1007/s00026-016-0325-x","extern":1,"year":"2016","publist_id":"6202","status":"public","citation":{"ista":"Hibi T, Solus LT. 2016. Facets of the r-stable (n, k)-hypersimplex. Annals of Combinatorics. 20(4), 815–829.","ieee":"T. Hibi and L. T. Solus, “Facets of the r-stable (n, k)-hypersimplex,” <i>Annals of Combinatorics</i>, vol. 20, no. 4. Springer, pp. 815–829, 2016.","short":"T. Hibi, L.T. Solus, Annals of Combinatorics 20 (2016) 815–829.","ama":"Hibi T, Solus LT. Facets of the r-stable (n, k)-hypersimplex. <i>Annals of Combinatorics</i>. 2016;20(4):815-829. doi:<a href=\"https://doi.org/10.1007/s00026-016-0325-x\">10.1007/s00026-016-0325-x</a>","chicago":"Hibi, Takayugi, and Liam T Solus. “Facets of the R-Stable (n, k)-Hypersimplex.” <i>Annals of Combinatorics</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00026-016-0325-x\">https://doi.org/10.1007/s00026-016-0325-x</a>.","apa":"Hibi, T., &#38; Solus, L. T. (2016). Facets of the r-stable (n, k)-hypersimplex. <i>Annals of Combinatorics</i>. Springer. <a href=\"https://doi.org/10.1007/s00026-016-0325-x\">https://doi.org/10.1007/s00026-016-0325-x</a>","mla":"Hibi, Takayugi, and Liam T. Solus. “Facets of the R-Stable (n, k)-Hypersimplex.” <i>Annals of Combinatorics</i>, vol. 20, no. 4, Springer, 2016, pp. 815–29, doi:<a href=\"https://doi.org/10.1007/s00026-016-0325-x\">10.1007/s00026-016-0325-x</a>."},"publication_status":"published","author":[{"last_name":"Hibi","first_name":"Takayugi","full_name":"Hibi, Takayugi"},{"first_name":"Liam T","last_name":"Solus","id":"2AADA620-F248-11E8-B48F-1D18A9856A87","full_name":"Liam Solus"}],"issue":"4","date_published":"2016-12-01T00:00:00Z","type":"journal_article","month":"12","acknowledgement":"Liam Solus was supported by a 2014 National Science Foundation/Japan Society for the Promotion of Science East Asia and Pacific Summer Institute Fellowship. \nOpen access funding provided by IST Austria."}