Flag subdivisions and<i>γ</i>-vectors

Christos A. Athanasiadis

Type: Article

Publication Date: 2012-10-03

Citations: 39

DOI: https://doi.org/10.2140/pjm.2012.259.257

Abstract

The γ -vector is an important enumerative invariant of a flag simplicial homology sphere.It has been conjectured by Gal that this vector is nonnegative for every such sphere and by Reiner, Postnikov and Williams that it increases when is replaced by any flag simplicial homology sphere that geometrically subdivides .Using the nonnegativity of the γ -vector in dimension 3, proved by Davis and Okun, as well as Stanley's theory of simplicial subdivisions and local h-vectors, the latter conjecture is confirmed in this paper in dimensions 3 and 4.

Locations

Pacific Journal of Mathematics - View - PDF

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+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota