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 Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 127–139 (Mi tm1873)

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.

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Proceedings of the Steklov Institute of Mathematics, 2009, 266, 120–132

Bibliographic databases:

UDC: 514.172.45+515.164.8

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, Tr. Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 127–139; Proc. Steklov Inst. Math., 266 (2009), 120–132

Citation in format AMSBIB
\Bibitem{Ero09} \by N.~Yu.~Erokhovets \paper Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs \inbook Geometry, topology, and mathematical physics.~II \bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2009 \vol 266 \pages 127--139 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm1873} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603264} \zmath{https://zbmath.org/?q=an:1227.52006} \transl \jour Proc. Steklov Inst. Math. \yr 2009 \vol 266 \pages 120--132 \crossref{https://doi.org/10.1134/S0081543809030079} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000270722100007} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350371240} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. D. Volodin, “Cubical realizations of flag nestohedra and proof of Gal's conjecture for them”, Russian Math. Surveys, 65:1 (2010), 188–190
2. V. M. Buchstaber, V. D. Volodin, “Sharp upper and lower bounds for nestohedra”, Izv. Math., 75:6 (2011), 1107–1133
3. Aisbett N., “Inequalities Between Gamma-Polynomials of Graph-Associahedra”, Electron. J. Comb., 19:2 (2012), P36
4. Aisbett N., “Frankl-Furedi-Kalai Inequalities on the Gamma-Vectors of Flag Nestohedra”, Discret. Comput. Geom., 51:2 (2014), 323–336
5. N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Proc. Steklov Inst. Math., 286 (2014), 128–187
6. V. M. Buchstaber, N. Yu. Erokhovets, “Truncations of simple polytopes and applications”, Proc. Steklov Inst. Math., 289 (2015), 104–133
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