Some parity results for 16-cores

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Kolitsch and Sellers showed recently that a8(n), the number of 8-core partitions of n, is even when n belongs to certain arithmetic progressions. We prove a similar result for 16-cores. In doing so, we prove the surprising result that the a16(n), given by ∑ a16(n) qn = (q16)16/(q), n≥0 satisfy a16(43046721n + 457371400) ≡ a16(n) (mod 2).

Original languageEnglish (US)
Pages (from-to)281-296
Number of pages16
JournalRamanujan Journal
Volume3
Issue number3
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

Keywords

  • Parity
  • T-cores

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