2024/02/19 by Frédéric Chapoton, Chapoton, Frédéric
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2402.11979
openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.