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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 266, Pages 127–139
(Mi tm1873)
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This article is cited in 8 scientific papers (total in 8 papers)
Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs
N. Yu. Erokhovets Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Abstract:
Convex polytopes have interested mathematicians since very ancient times. At present, they occupy a central place in convex geometry, combinatorics, and toric topology and demonstrate the harmony and beauty of mathematics. This paper considers the problem of describing the $f$-vectors of simple flag polytopes, that is, simple polytopes in which any set of pairwise intersecting facets has nonempty intersection. We show that for each nestohedron corresponding to a connected building set, the $h$-polynomial is a descent-generating function for some class of permutations; we also prove Gal's conjecture on the nonnegativity of $\gamma$-vectors of flag polytopes for nestohedra constructed over complete bipartite graphs.
Received in February 2009
Citation:
N. Yu. Erokhovets, “Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 127–139; Proc. Steklov Inst. Math., 266 (2009), 120–132
Linking options:
https://www.mathnet.ru/eng/tm1873 https://www.mathnet.ru/eng/tm/v266/p127
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Abstract page: | 362 | Full-text PDF : | 76 | References: | 63 |
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