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

Mathematics

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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title = "Elementary proofs of infinitely many congruences for 8-cores",

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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T1 - Elementary proofs of infinitely many congruences for 8-cores

AU - Kolitsch, Louis W.

AU - Sellers, James A.

PY - 1999

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N2 - 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.

AB - 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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UR - https://www.scopus.com/pages/publications/22644448737#tab=citedBy

U2 - 10.1023/A:1006953609540

DO - 10.1023/A:1006953609540

M3 - Article

AN - SCOPUS:22644448737

SN - 1382-4090

VL - 3

SP - 221

EP - 226

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

Elementary proofs of infinitely many congruences for 8-cores

Abstract

All Science Journal Classification (ASJC) codes

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