Geodesic
Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs
Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 127-139

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2009_266_a6,
     author = {N. Yu. Erokhovets},
     title = {Gal's {Conjecture} for {Nestohedra} {Corresponding} to {Complete} {Bipartite} {Graphs}},
     journal = {Informatics and Automation},
     pages = {127--139},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a6/}
}
TY  - JOUR
AU  - N. Yu. Erokhovets
TI  - Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs
JO  - Informatics and Automation
PY  - 2009
SP  - 127
EP  - 139
VL  - 266
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a6/
LA  - ru
ID  - TRSPY_2009_266_a6
ER  - 
%0 Journal Article
%A N. Yu. Erokhovets
%T Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs
%J Informatics and Automation
%D 2009
%P 127-139
%V 266
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a6/
%G ru
%F TRSPY_2009_266_a6
N. Yu. Erokhovets. Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs. Informatics and Automation, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 127-139. http://geodesic.mathdoc.fr/item/TRSPY_2009_266_a6/