English

A combinatorial proof of the Alladi-Gordon key identity for Schur's partition theorem

Combinatorics 2012-02-07 v1

Abstract

The Alladi-Gordon identity plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by establishing an involution on the underlying set of overpartitions.

Keywords

Cite

@article{arxiv.1202.1219,
  title  = {A combinatorial proof of the Alladi-Gordon key identity for Schur's partition theorem},
  author = {James J. Y. Zhao},
  journal= {arXiv preprint arXiv:1202.1219},
  year   = {2012}
}

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9 pages