Determinants Associated to Zeta Matrices of Posets
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2004
- DOI:
- 10.48550/arXiv.math/0403401
- arXiv:
- arXiv:math/0403401
- Bibcode:
- 2004math......3401B
- Keywords:
-
- Combinatorics;
- 05C20;
- 05C50;
- 06A11;
- 15A15
- E-Print:
- 14 pages, AMS-TeX