For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric ideal IG ⊂ R such that R/IG has (Castelnuovo-Mumford) regularity r and h-polynomial of degree d. To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O'Keefe that compares the depth and dimension of toric ideals of graphs.

Regularity and h-polynomials of toric ideals of graphs / Favacchio, G.; Keiper, G.; Van Tuyl, A.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 148:11(2020), pp. 4665-4677. [10.1090/proc/15126]

Regularity and h-polynomials of toric ideals of graphs

Favacchio G.;
2020

Abstract

For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric ideal IG ⊂ R such that R/IG has (Castelnuovo-Mumford) regularity r and h-polynomial of degree d. To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O'Keefe that compares the depth and dimension of toric ideals of graphs.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2859714