Bialgebras of recursive sequences and combinatorial identities

  • Authors:

  • Carl A. Futia;Eric F. Müller;Earl J. Taft

  • Affiliations:

  • 5501 Keeney Street, Morton Grove, Illinois;Mathematisches Institut, Universität München, Theresienstrasse 39, D-80333 Munich, Germany;Department of Mathematics, Rutgers University, Piscataway, New Jersey

  • Venue:
  • Advances in Applied Mathematics
  • Year:
  • 2002

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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.