scholarly journals POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES

2021 ◽  
pp. 1-23
Author(s):  
VIVIANA ENE ◽  
GIANCARLO RINALDO ◽  
NAOKI TERAI
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Edge Ideals ◽  
Block Graphs

Abstract We study powers of binomial edge ideals associated with closed and block graphs.

scholarly journals Weakly Closed Graphs and F-Purity of Binomial Edge Ideals

2018 ◽  
Vol 25 (04) ◽  
pp. 567-578
Author(s):  
Kazunori Matsuda
Keyword(s):  
Polynomial Ring ◽  
Quotient Ring ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Edge Ideal ◽  
Closed Graph ◽  
Edge Ideals ◽  
Weakly Closed

Herzog, Hibi, Hreindóttir et al. introduced the class of closed graphs, and they proved that the binomial edge ideal JG of a graph G has quadratic Gröbner bases if G is closed. In this paper, we introduce the class of weakly closed graphs as a generalization of the closed graph, and we prove that the quotient ring S/JG of the polynomial ring [Formula: see text] with K a field and [Formula: see text] is F-pure if G is weakly closed. This fact is a generalization of Ohtani’s theorem.

scholarly journals Binomial Edge Ideals with Quadratic Gröbner Bases

10.37236/698 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Marilena Crupi ◽  
Giancarlo Rinaldo
Keyword(s):  
Gröbner Basis ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Edge Ideal ◽  
Grobner Basis ◽  
Edge Ideals ◽  
Term Order ◽  
Vertex Set

We prove that a binomial edge ideal of a graph $G$ has a quadratic Gröbner basis with respect to some term order if and only if the graph $G$ is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph $G$ that do not depend on the labelling of its vertex set.

scholarly journals Gröbner bases for operads

2010 ◽  
Vol 153 (2) ◽  
pp. 363-396 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Anton Khoroshkin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases

scholarly journals Gröbner bases over fields with valuations

2018 ◽  
Vol 88 (315) ◽  
pp. 467-483 ◽  
Author(s):  
Andrew J. Chan ◽  
Diane Maclagan
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases
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