40 citations · 95 across the 43 of their papers we have counts for
6 papers · 1 filter
Cohen-Macaulay Circulant Graphs
Kevin N. Vander Meulen, Adam Van Tuyl, Catriona Watt
Let G be the circulant graph C_n(S) with S a subset of {1,2,...,\lfloor n/2 \rfloor}, and let I(G) denote its the edge ideal in the ring R = k[x_1,...,x_n]. We consider the problem…
Partial coloring, vertex decomposability, and sequentially Cohen-Macaulay simplicial complexes
Jennifer Biermann, Christopher A. Francisco, Huy Tài Hà +1
In attempting to understand how combinatorial modifications alter algebraic properties of monomial ideals, several authors have investigated the process of adding "whiskers" to gra…
Classifying ACM sets of points in via separators
Elena Guardo, Adam Van Tuyl
The purpose of this note is to give a new, short proof of a classification of ACM sets of points in in terms of separators.
Star configurations on generic hypersurfaces
Enrico Carlini, Elena Guardo, Adam Van Tuyl
Let be a homogeneous polynomial in . Our goal is to understand a particular polynomial decomposition of ; geometrically, we wish to determine wh…
Asymptotic resurgences for ideals of positive dimensional subschemes of projective space
Elena Guardo, Brian Harbourne, Adam Van Tuyl
Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of determining which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bo…
Balanced vertex decomposable simplicial complexes and their h-vectors
Jennifer Biermann, Adam Van Tuyl
Given any finite simplicial complex Δ, we show how to construct a new simplicial complex Δ_χ that is balanced and vertex decomposable. Moreover, we show that the h-vector of the si…