Marking and shifting a part in partition theorems
Combinatorics
2018-09-11 v1
Abstract
Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identities, Euler's odd=distinct theorem, and the Andrews-Gordon identities. Generalizations of each of these theorems are given where a single part is "marked" or weighted. This allows a single part to be replaced by a new larger part, "shifting" a part, and analogous combinatorial results are given in each case. Versions are also given for marking a sum of parts.
Cite
@article{arxiv.1809.02685,
title = {Marking and shifting a part in partition theorems},
author = {Kathleen O'Hara and Dennis Stanton},
journal= {arXiv preprint arXiv:1809.02685},
year = {2018}
}