Resolutions of square-free monomial ideals via facet ideals: a survey

By Huy Tài Hà, Adam Van Tuyl. 2006

72 citations recorded by the source corpus.

We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets) of a simplicial complex \Delta.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7e4977ee66ff5a2623ed73c901c9be25623a9b8a

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Algebraic study on Cameron-Walker graphs (2013, background): “Recently, edge ideals of finite simple graphs have been studied by many authors from viewpoints of computational commutative algebra and combinatorics; see [8, 14, 17], and their references.”
The regularity of powers of edge ideals (2014, background): “Bounds on the regularity of edge ideals have been studied by a number of researchers (see [1], [2], [3], [4], [5], [6], [7],[8] [9], [11],[12],[13]).”
A Beginner’s Guide to Edge and Cover Ideals (2013, background): “If you are interested in learning more, I would recommend that your reading list include Villarreal’s textbook [64] (especially Chapter 6), Herzog and Hibi’s text [36] (in particular, Chapter 9), the recent survey of Morey and Villarreal [50], and an older survey of Hà and the author [33].”
Embedded Associated Primes of Powers of Square-free Monomial Ideals (2008, background): “[9, 13, 22]), and has appeared in the literature (cf.”
Non-vanishingness of Betti numbers of edge ideals (2011, background): “For other problems and results on this area we refer to [6].”
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers (2006, background): “A C ] 2 8 M ay 2 00 Dedicated to Anthony V. Geramita on the occasion of his 65th birthday.”
Regularity 3 in edge ideals associated to bipartite graphs (2012, background): “) associated to them is a well known technique that has been fruitfully exploited in the last decades (see for example the surveys [12] and [15] and their references).”