Generalizations of Abel's and Hurwitz's identities

  • Authors:

  • Alexander Kelmans;Alexander Postnikov

  • Affiliations:

  • University of Puerto Rico, San Juan, PR, United States and Rutgers University, New Brunswick, NJ, United States;Massachusetts Institute of Technology, Cambridge, MA, United States

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2008

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Abstract

In 1826 N. Abel found a generalization of the binomial formula. In 1902 Abel's theorem was further generalized by A. Hurwitz. In this paper we describe constructions that provide infinitely many identities each being a generalization of a Hurwitz's identity. Moreover, we give combinatorial interpretations of all these identities as the forest volumes of certain directed graphs.