Linked partition ideals and the Alladi--Schur theorem
Combinatorics
2021-10-27 v1 Number Theory
Abstract
Let denote the set of integer partitions into parts that differ by at least , with the added constraint that no two consecutive multiples of occur as parts. We derive trivariate generating functions of Andrews--Gordon type for partitions in with both the number of parts and the number of even parts counted. In particular, we provide an analytic counterpart of Andrews' recent refinement of the Alladi--Schur theorem.
Cite
@article{arxiv.2110.13247,
title = {Linked partition ideals and the Alladi--Schur theorem},
author = {George E. Andrews and Shane Chern and Zhitai Li},
journal= {arXiv preprint arXiv:2110.13247},
year = {2021}
}