Combinatorial g-conjecture for interval subdivisions. Issue 5 (4th May 2022) - Anwar, Imran; Nazir, Shaheen
Abstract: We verify the g -conjecture for interval subdivisions of Cohen–Macaulay simplicial complexes, using purely combinatorial methods. More precisely, we show that the g -vector of the interval subdivision of a Cohen–Macaulay simplicial complex is an f -vector. Murai defined the g ″ -vector, starting from the h ″ -vector introduced by Novik for Buchsbaum simplicial complexes. We prove that the g ″ -vector of the interval subdivision of a Buchsbaum simplicial complex is an f -vector of some simplicial complex.