72 citations · 78 across the 11 of their papers we have counts for
13 papers
Symbolic powers and integral closures via extremal ideals
Trung Chau, Art Duval, Sara Faridi +3
This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…
Realizing resolutions of powers of extremal ideals
Trung Chau, Art M. Duval, Sara Faridi +3
Extremal ideals are a class of square-free monomial ideals which dominate and determine many algebraic invariants of powers of all square-free monomial ideals. For example, the $r^…
Simplicial effective resistance and enumeration of spanning trees
Art M. Duval, Woong Kook, Kang-Ju Lee +1
A graph can be regarded as an electrical network in which each edge is a resistor. This point of view relates combinatorial quantities, such as the number of spanning trees, to ele…
A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes
Ghodratollah Aalipour, Art M. Duval, Woong Kook +2
We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of…
Simplicial and Cellular Trees
Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of d…
A non-partitionable Cohen-Macaulay simplicial complex
Art M. Duval, Bennet Goeckner, Caroline J. Klivans +1
A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. D…