--- res: bibo_abstract: - "In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Sergey foaf_name: Avvakumov, Sergey foaf_surname: Avvakumov foaf_workInfoHomepage: http://www.librecat.org/personId=3827DAC8-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Roman foaf_name: Karasev, Roman foaf_surname: Karasev bibo_doi: 10.48550/arXiv.1907.11183 dct_date: 2019^xs_gYear dct_language: eng dct_title: Envy-free division using mapping degree@ ...