Determinants Associated to Zeta Matrices of Posets

Cristina M. Ballantine; Sharon M. Frechette; John B. Little

Determinants Associated to Zeta Matrices of Posets

Combinatorics 2007-05-23 v1

Authors: Cristina M. Ballantine , Sharon M. Frechette , John B. Little

Abstract

We consider the matrix ${\frak Z}_P=Z_P+Z_P^t$ , where the entries of $Z_P$ are the values of the zeta function of the finite poset $P$ . We give a combinatorial interpretation of the determinant of ${\frak Z}_P$ and establish a recursive formula for this determinant in the case in which $P$ is a boolean algebra.

Keywords

poset zeta matrix determinant boolean algebra combinatorial interpretation

Cite

@article{arxiv.math/0403401,
  title  = {Determinants Associated to Zeta Matrices of Posets},
  author = {Cristina M. Ballantine and Sharon M. Frechette and John B. Little},
  journal= {arXiv preprint arXiv:math/0403401},
  year   = {2007}
}

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14 pages, AMS-TeX

Determinants Associated to Zeta Matrices of Posets

Abstract

Keywords

Cite

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