Adam Van Tuyl

activity

20122020

most citedThe regularity of some families of circulant graphs

8 citations · 9 across the 3 of their papers we have counts for

collaborators

6 papers

math.AC2020

Powers of Principal $Q$ -Borel ideals

Eduardo Camps Moreno, Craig Kohne, Eliseo Sarmiento +1

Fix a poset $Q$ on ${x_{1}, \dots, x_{n}}$ . A $Q$ -Borel monomial ideal $I \subseteq K [x_{1}, \dots, x_{n}]$ is a monomial ideal whose monomials are closed under the Borel-like mov…

math.AC2020★ 1 cited

Homological invariants of Cameron--Walker graphs

Takayuki Hibi, Hiroju Kanno, Kyouko Kimura +2

Let $G$ be a finite simple connected graph on $[n]$ and $R = K [x_{1}, \dots, x_{n}]$ the polynomial ring in $n$ variables over a field $K$ . The edge ideal of $G$ is the ideal $I (G)$ o…

math.AC2019

Splittings of Toric Ideals

Giuseppe Favacchio, Johannes Hofscheier, Graham Keiper +1

Let $I \subseteq R = K [x_{1}, \dots, x_{n}]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric…

math.AC2019★ 8 cited

The regularity of some families of circulant graphs

Miguel Eduardo Uribe-Paczka, Adam Van Tuyl

We compute the Castelnuovo-Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to com…

math.CO2019

Maximum nullity and zero forcing of circulant graphs

Linh Duong, Brenda K. Kroschel, Michael Riddell +2

It is well-known that the zero forcing number of a graph provides a lower bound on the minimum rank of a graph. In this paper we bound and characterize the zero forcing number of c…

math.AC2012

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…