On a q-analogue of the Zeta polynomial of posets
Sur un q-analogue du polynôme Zeta des ordres partiels
Résumé
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.
Domaines
Combinatoire [math.CO]| Origine | Fichiers produits par l'(les) auteur(s) |
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