Elementary proofs of infinitely many congruences for 8-cores

Louis W. Kolitsch; James A. Sellers

doi:10.1023/A:1006953609540

Elementary proofs of infinitely many congruences for 8-cores

Louis W. Kolitsch, James A. Sellers

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

17 Scopus citations

Abstract

Using a very elementary argument, we prove the congruences a₈(81n + 21) ≡ 0 (mod 2) and a₈(81n + 75) ≡ 0 (mod 2) where a₈(n) is the number of 8-core partitions of n. We also exhibit two infinite families of congruences modulo 2 for 8-cores.

Original language	English (US)
Pages (from-to)	221-226
Number of pages	6
Journal	Ramanujan Journal
Volume	3
Issue number	2
DOIs	https://doi.org/10.1023/A:1006953609540
State	Published - 1999
Externally published	Yes

Keywords

Congruences
Partitions
t-cores

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abstract = "Using a very elementary argument, we prove the congruences a8(81n + 21) ≡ 0 (mod 2) and a8(81n + 75) ≡ 0 (mod 2) where a8(n) is the number of 8-core partitions of n. We also exhibit two infinite families of congruences modulo 2 for 8-cores.",

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KW - Congruences

KW - Partitions

KW - t-cores

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Elementary proofs of infinitely many congruences for 8-cores

Abstract

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