2011/06/22 by Athanasiadis, Christos A.
#05E45 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1106.4520
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 Δ and by Reiner, Postnikov and Williams that it increases when Δ is replaced by any flag simplicial homology sphere which geometrically subdivides Δ. 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.