Loading...
Pseudodeterminants and Perfect Square Spanning Tree Counts
Martin, Jeremy L. Maxwell, Molly Reiner, Victor Wilson, Scott O.
Martin, Jeremy L.
Maxwell, Molly
Reiner, Victor
Wilson, Scott O.
Citations
Altmetric:
Abstract
The pseudodeterminant pdet(M) of a square matrix is the last nonzero coe cient in its characteristic
polynomial; for a nonsingular matrix, this is just the determinant. If @ is a symmetric or skewsymmetric
matrix then pdet(@@t) = pdet(@)2. Whenever @ is the kth boundary map of a self-dual CWcomplex
X, this linear-algebraic identity implies that the torsion-weighted generating function for cellular
k-trees in X is a perfect square. In the case that X is an antipodally self-dual CW-sphere of odd dimension,
the pseudodeterminant of its kth cellular boundary map can be interpreted directly as a torsion-weighted
generating function both for k-trees and for (k 1)-trees, complementing the analogous result for evendimensional
spheres given by the second author. The argument relies on the topological fact that any
self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.
Description
This is the author's final draft. Copyright 2015 International Press.
Date
2015-06
Journal Title
Journal ISSN
Volume Title
Publisher
International Press
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
Martin, Jeremy L., Molly Maxwell, Victor Reiner, and Scott O. Wilson. "Pseudodeterminants and Perfect Square Spanning Tree Counts." Journal of Combinatorics 6.3 (2015): 295-325. DOI: