Geodesic
Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 127-139

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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{TM_2009_266_a6,
     author = {N. Yu. Erokhovets},
     title = {Gal's {Conjecture} for {Nestohedra} {Corresponding} to {Complete} {Bipartite} {Graphs}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {127--139},
     publisher = {mathdoc},
     volume = {266},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a6/}
}
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N. Yu. Erokhovets. Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 127-139. http://geodesic.mathdoc.fr/item/TM_2009_266_a6/