Marking and Shifting a Part in Partitions

Kathleen O’Hara, Dennis Stanton

Research output: Contribution to journalArticlepeer-review


Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers–Ramanujan identities, the Göllnitz–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.

Original languageEnglish (US)
Pages (from-to)935-951
Number of pages17
JournalAnnals of Combinatorics
Issue number3-4
StatePublished - Nov 1 2019


  • Partition
  • Rogers–Ramanujan identities


Dive into the research topics of 'Marking and Shifting a Part in Partitions'. Together they form a unique fingerprint.

Cite this