72 citations · 78 across the 11 of their papers we have counts for
10 papers · 1 filter
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…
Cuts and flows of cell complexes
Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical…
Critical groups of simplicial complexes
Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinat…