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On a q-analogue of the Zeta polynomial of posets (2402.11979v2)
Published 19 Feb 2024 in math.CO
Abstract: We introduce a q-analogue of the classical Zeta polynomial of finite partially ordered sets, as a polynomial in one variable x with coefficients depending on the indeterminate q. We prove some properties of this polynomial invariant, including its behaviour with respect to duality, product and disjoint union. The leading term is a q-analogue of the number of maximal chains, but not always with non-negative coefficients. The value at q=0 turns out to be essentially the characteristic polynomial.
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