Abstract
A polynomially recursive sequence satisfies a recursive relation with variable coefficients. The set of these sequences has the structure of a topological bialgebra. If such a sequence is of a combinatorial nature, a formula for its coproduct can (upon appropriate evaluation) be interpreted as a combinatorial identity. Here we give a coproduct formula for each sequence , one for each t ≥ 0, and its interpretation as a combinatorial identity. We also obtain a q-version of this coproduct formula and combinatorial identity.
Notes
Communicated by S. Montgomery.
We dedicate this article to Miriam Cohen in honor of her outstanding contributions to the field of Hopf algebras.