Sequentially Cohen-Macaulay edge ideals
- Christopher A. Francisco, A. Tuyl
- Mathematics
- 1 November 2005
Let G be a simple undirected graph on n vertices, and let I(G) C R = k[x 1 ,...,x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof…
Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers
- Huy Tài Hà, A. Tuyl
- Mathematics
- 21 June 2006
Abstract
We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to…
Shellable graphs and sequentially Cohen-Macaulay bipartite graphs
- A. Tuyl, R. Villarreal
- MathematicsJournal of combinatorial theory. Series A
- 10 January 2007
Splittings of monomial ideals
- Christopher A. Francisco, Huy Tài Hà, A. Tuyl
- Mathematics
- 14 July 2008
We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and…
Sequentially Cohen–Macaulay bipartite graphs: vertex decomposability and regularity
- A. Tuyl
- Mathematics
- 1 June 2009
Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen–Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the…
Balanced Vertex Decomposable Simplicial Complexes and their h-vectors
- Jennifer Biermann, A. Tuyl
- MathematicsElectronic Journal of Combinatorics
- 31 January 2012
A new equivalent statement to a theorem of Bjorner, Frankl, and Stanley that classifies the f-vectors of simplicial complexes is added, which proves a special case of a conjecture of Cook and Nagel, and Constantinescu and Varbaro on the h-vector of flag complexes.
The symbolic defect of an ideal
- Federico Galetto, A. Geramita, Y. Shin, A. Tuyl
- MathematicsJournal of Pure and Applied Algebra
- 1 October 2016
Splittable ideals and the resolutions of monomial ideals
- Huy Tài Hà, A. Tuyl
- Mathematics
- 10 March 2005
Associated primes of monomial ideals and odd holes in graphs
- Christopher A. Francisco, Huy Tài Hà, A. Tuyl
- Mathematics
- 6 June 2008
Let G be a finite simple graph with edge ideal I(G). Let I(G)∨ denote the Alexander dual of I(G). We show that a description of all induced cycles of odd length in G is encoded in the associated…
Multigraded Regularity: Syzygies and Fat Points
The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connec-…
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