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Parity considerations in Andrews–Gordon identities

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
31
Issue
3
Identifiers
DOI: 10.1016/j.ejc.2009.06.002
Disciplines
  • Mathematics

Abstract

Abstract In 1974, Andrews discovered the generating function for the partitions of n considered in a theorem due to Gordon. In a more recent paper, he reconsidered this generating function and gave refinements where additional restrictions involving parities are imposed. A combinatorial construction for the partitions enumerated by the mentioned generating function is given. Some of the Andrews’ refinements are proven combinatorially, and a conjecture of his is settled.

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