Current Trends on Monomial and Binomial Ideals

• Main Author: Hibi, Takayuki (auth)
• Other Authors: H (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Subjects: edge ideal; flawless; Cohen Macaulay; dstab; partially ordered set; Stanley depth; associated graded rings; stable set polytope; Stanley-Reisner ideal; linear part; stable set polytopes; order and chain polytopes; Gröbner bases; distribuive lattice; Cohen-Macaulay; depth of powers of bipartite graphs; directed cycle; Rees algebra; toric ideals; polymatroidal ideal; graph; toric ring; Stanley-Reisner ring; Castelnuovo-Mumford regularity; chain polytope; complete intersection; symbolic power; circuit; h-vector; multipartite graph; monomial ideal; regular elements on powers of bipartite graphs; syzygy; projective dimension; regularity; Betti number; (S2) condition; graphs; integral closure; edge ring; edge polytope; Stanley's inequality; O-sequence; algebras with straightening laws; order polytope; circulant graphs; bipartite graph; cover ideal; edge ideals; even cycle; depth; colon ideals; matching number; Bipartite graphs
• Online Access: DOAB: download the publication; DOAB: description of the publication

Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commut...