A congruence modulo 3 for partitions into distinct non-multiples of four

Michael D. Hirschhorn, James Allen Sellers

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In 2001, Andrews and Lewis utilized an identity of F. H. Jackson to derive some new partition generating functions as well as identities involving some of the corresponding partition functions. In particular, for 0 < a < b < k, they defined W1(a, b; k; n) to be the number of partitions of n in which the parts are congruent to a or b mod k and such that, for any j, kj + a and kj + b are not both parts. Our primary goal in this note is to prove that W1(1, 3; 4; 27n + 17) ≡ 0 (mod 3) for all n ≥ 0. We prove this result using elementary generating function manipulations and classic results from the theory of partitions.

Original languageEnglish (US)
Article number14.9.6
JournalJournal of Integer Sequences
Volume17
Issue number9
StatePublished - Sep 4 2014

Fingerprint

Partition Function
Congruence
Generating Function
Modulo
Partition
Distinct
Elementary Functions
Congruent
Manipulation

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

Hirschhorn, Michael D. ; Sellers, James Allen. / A congruence modulo 3 for partitions into distinct non-multiples of four. In: Journal of Integer Sequences. 2014 ; Vol. 17, No. 9.
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A congruence modulo 3 for partitions into distinct non-multiples of four. / Hirschhorn, Michael D.; Sellers, James Allen.

In: Journal of Integer Sequences, Vol. 17, No. 9, 14.9.6, 04.09.2014.

Research output: Contribution to journalArticle

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