Some parity results for 16-cores

Michael D. Hirschhorn, James A. Sellers

Research output: Contribution to journalArticle

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

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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    Hirschhorn, M. D., & Sellers, J. A. (1999). Some parity results for 16-cores. Ramanujan Journal, 3(3), 281-296. https://doi.org/10.1023/A:1009879303577