Show simple item record

dc.contributor.authorMartin, Jeremy L.
dc.contributor.authorMaxwell, Molly
dc.contributor.authorReiner, Victor
dc.contributor.authorWilson, Scott O.
dc.identifier.citationMartin, 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:en_US
dc.descriptionThis is the author's final draft. Copyright 2015 International Press.en_US
dc.description.abstractThe 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.en_US
dc.publisherInternational Pressen_US
dc.titlePseudodeterminants and Perfect Square Spanning Tree Countsen_US
kusw.kuauthorMartin, Jeremy L.
kusw.oanotesPer SHERPA/RoMEO 9/25/15: Author's Pre-print: green tick author can archive pre-print (ie pre-refereeing) Author's Post-print: green tick author can archive post-print (ie final draft post-refereeing) Publisher's Version/PDF: No information archiving status unknown General Conditions:

On a non-profit server Published source must be acknowledged Publisher's copyright must be acknowledged where this has been assigned
kusw.oaversionScholarly/refereed, author accepted manuscript
kusw.oapolicyThis item meets KU Open Access policy criteria.

Files in this item


This item appears in the following Collection(s)

Show simple item record