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