Some parity results for 16-cores

Michael D. Hirschhorn; James A. Sellers

doi:10.1023/A:1009879303577

Some parity results for 16-cores

Michael D. Hirschhorn
, James A. Sellers

Mathematics

Research output: Contribution to journal › Article › peer-review

20 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 language	English (US)
Pages (from-to)	281-296
Number of pages	16
Journal	Ramanujan Journal
Volume	3
Issue number	3
DOIs	https://doi.org/10.1023/A:1009879303577
State	Published - 1999

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1023/A:1009879303577

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title = "Some parity results for 16-cores",

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).",

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AU - Hirschhorn, Michael D.

AU - Sellers, James A.

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AB - 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).

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DO - 10.1023/A:1009879303577

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Some parity results for 16-cores

Abstract

All Science Journal Classification (ASJC) codes

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