Lakehead University

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most citedEvolution of Semantic Similarity -- A Survey

300 citations

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17 papers · 1 filter

math.AC2009★ 1 cited

Separators of fat points in P^n x P^m

Elena Guardo, Adam Van Tuyl

We introduce definitions for the separator of a fat point and the degree of a fat point for a fat point scheme Z in P^n x P^m, and we study some of their properties.

math.AC2009★ 1 cited

Sequentially Cohen-Macaulay bipartite graphs: vertex decomposability and regularity

Adam Van Tuyl

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,…

math.AC2009★ 7 cited

Algebraic properties of the path ideal of a tree

Jing Jane He, Adam Van Tuyl

The path ideal (of length t >=2) of a graph G is the monomial ideal, denoted I_t(G), whose generators correspond to the directed paths of length t in G. We study some of the algebr…

math.AC2008

Splittings of monomial ideals

Christopher A. Francisco, Huy Tai Ha, Adam Van Tuyl

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 E…

math.AC2008★ 2 cited

Associated primes of monomial ideals and odd holes in graphs

Christopher A. Francisco, Huy Tai Ha, Adam Van Tuyl

Let $G$ be a finite simple graph with edge ideal $I (G)$ . Let $J (G)$ denote the Alexander dual of $I (G)$ . We show that a description of all induced cycles of odd length in $G$ is en…

math.AC2007

Simplicial complexes and Macaulay's inverse systems

Adam Van Tuyl, Fabrizio Zanello

Let $Δ$ be a simplicial complex on $V = {x_{1}, ..., x_{n}}$ , with Stanley-Reisner ideal $I_{Δ} \subseteq R = k [x_{1}, ..., x_{n}]$ . The goal of this paper is to investigate the class of artini…