Combinatorial g-conjecture for interval subdivisions. Issue 5 (4th May 2022)

• Record Type: Journal Article
• Authors: Anwar, Imran; Nazir, Shaheen
• Is Part Of: Communications in algebra. Volume 50:Issue 5(2022)
• Page Start: 1889
• Page End: 1905
• Publication Date: 2022-05-04
• Subjects: g-Vector -- h-vector -- simplicial complex -- subdivision of a simplicial complex; 05E45 -- 52B05 -- 05A05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1993236
• Languages: English
• ISSNs: 0092-7872

Abstract

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.