zbMATH — the first resource for mathematics

Bounds for entries of \(\gamma\)-vectors of flag homology spheres. (English) Zbl 1441.05253

05E45 Combinatorial aspects of simplicial complexes
52B70 Polyhedral manifolds
05C35 Extremal problems in graph theory
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
Full Text: DOI
[1] M. Adamaszek and J. Hladký, Upper bound theorem for odd-dimensional flag triangulations of manifolds, Mathematika, 62 (2016), pp. 909–928. · Zbl 1347.05254
[2] N. Aisbett, Gamma-vectors of edge subdivisions of the boundary of the cross-polytope, preprint, , 2012.
[3] L. J. Billera and C. W. Lee, Sufficiency of McMullen’s conditions for \(f\)-vectors of simplicial polytopes, Bull. Amer. Math. Soc. (N.S.), 2 (1980), pp. 181–185. · Zbl 0431.52009
[4] P. Brinkmann and G. M. Ziegler, A flag vector of a 3-sphere that is not the flag vector of a 4-polytope, Mathematika, 63 (2017), pp. 260–271. · Zbl 1365.52012
[5] R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math., 171 (1995), pp. 117–137. · Zbl 0865.53036
[6] Ś. R. Gal, Real root conjecture fails for five- and higher-dimensional spheres, Discrete Comput. Geom., 34 (2005), pp. 269–284. · Zbl 1085.52005
[7] G. Kalai, Some aspects of the combinatorial theory of convex polytopes, in Polytopes: Abstract, Convex and Computational (Scarborough, ON, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 440, Kluwer Acad., Dordrecht, 1994, pp. 205–229. · Zbl 0804.52006
[8] V. Klee, A combinatorial analogue of Poincaré’s duality theorem, Canad. J. Math., 16 (1964), pp. 517–531. · Zbl 0134.42403
[9] F. H. Lutz and E. Nevo, Stellar theory for flag complexes, Math. Scand., 118 (2016), pp. 70–82. · Zbl 1350.57027
[10] R. Meshulam, Domination numbers and homology, J. Combin. Theory Ser. A, 102 (2003), pp. 321–330. · Zbl 1030.05086
[11] S. Murai and E. Nevo, On the cd-index and \(γ\)-vector of \({\rm S}^*\)-shellable CW-spheres, Math. Z., 271 (2012), pp. 1309–1319. · Zbl 1256.52006
[12] S. Murai and E. Nevo, On the generalized lower bound conjecture for polytopes and spheres, Acta Math., 210 (2013), pp. 185–202. · Zbl 1279.52014
[13] E. Nevo, Higher minors and Van Kampen’s obstruction, Math. Scand., 101 (2007), pp. 161–176. · Zbl 1163.57018
[14] E. Nevo and E. Novinsky, A characterization of simplicial polytopes with \(g_2=1\), J. Combin. Theory Ser. A, 118 (2011), pp. 387–395. · Zbl 1209.52007
[15] E. Nevo and T. K. Petersen, On \(γ\)-vectors satisfying the Kruskal-Katona inequalities, Discrete Comput. Geom., 45 (2011), pp. 503–521. · Zbl 1231.52009
[16] E. Nevo, T. K. Petersen, and B. E. Tenner, The \(γ\)-vector of a barycentric subdivision, J. Combin. Theory Ser. A, 118 (2011), pp. 1364–1380. · Zbl 1231.05307
[17] T. K. Petersen, Eulerian Numbers, Birkhäuser Adv. Texts Basler Lehrbücher, Birkhäuser/Springer, New York, 2015.
[18] R. P. Stanley, The number of faces of a simplicial convex polytope, Adv. Math., 35 (1980), pp. 236–238. · Zbl 0427.52006
[19] R. P. Stanley, Combinatorics and Commutative Algebra, 2nd ed., Progr. Mathematics 41, Birkhäuser Boston, Boston, MA, 1996. · Zbl 0838.13008
[20] V. D. Volodin, Cubical realizations of flag nestohedra and a proof of Gal’s conjecture for them, Uspekhi Mat. Nauk, 65 (2010), pp. 183–184. · Zbl 1204.52014
[21] H. Zheng, The flag upper bound theorem for 3- and 5-manifolds, Israel J. Math., to appear. · Zbl 1384.57014
[22] G. M. Ziegler, Lectures on Polytopes, Grad. Texts in Math. 152, Springer, New York, 1995.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.