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 -vector, starting from the
-vector introduced by Novik for Buchsbaum simplicial complexes. We prove that the
-vector of the interval subdivision of a Buchsbaum simplicial complex is an f-vector of some simplicial complex.
Acknowledgments
We are deeply indebted to anonymous referee for his/her comments and suggestions based on careful observations on the earlier version, which improved this paper in a great deal.