Bialgebras of recursive sequences and combinatorial identities

Abstract

A recursive sequence is an infinite sequence of elements of some fixed ground field which satisfies a recursion relation of finite order. We shall investigate certain bialgebra structures on linear spaces of recursive sequences. By choosing appropriate bases for these bialgebras we show how an explicit formula for the coproduct can imply interesting combinatorial identities. © 2002 Elsevier Science (USA).