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    Pseudodeterminants and Perfect Square Spanning Tree Counts

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    pseudodeterminants-revised-1.pdf (410.6Kb)
    Issue Date
    2015-06
    Author
    Martin, Jeremy L.
    Maxwell, Molly
    Reiner, Victor
    Wilson, Scott O.
    Publisher
    International Press
    Type
    Article
    Article Version
    Scholarly/refereed, author accepted manuscript
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    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.
    URI
    http://hdl.handle.net/1808/18512
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    • Mathematics Scholarly Works [282]
    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:

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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