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Determinants Associated to Zeta Matrices of Posets
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math.CO
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determinantfrakzetaalgebraassociatedbooleancasecombinatorial
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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.
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