English

Schmidt-type theorems for partitions with uncounted parts

Combinatorics 2022-07-15 v2

Abstract

Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain specifications may be a generally useful tool for establishing sum-product qq-series identities, examples of which are given.

Keywords

Cite

@article{arxiv.2203.05202,
  title  = {Schmidt-type theorems for partitions with uncounted parts},
  author = {George E. Andrews and William J. Keith},
  journal= {arXiv preprint arXiv:2203.05202},
  year   = {2022}
}

Comments

21 pages; Thereom 3 generalized; recent citations added. Version to be submitted

R2 v1 2026-06-24T10:08:18.484Z