Congruences for a restricted m-ary partition function

Laura L. Dolph, Annmarie Reynolds, James Allen Sellers

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We discuss a family of restricted m-ary partition functions bm,j(n), which is the number of m-ary partitions of n with at most i + j copies of the part mi allowed. We then use generating function dissections to prove the following family of congruences for k ≥ 2 and 1≤t≤m-k + 1: bm,m-1(mk+1n + mk+t-1 + mk+t-2 + ⋯ + mk) ≡ 0 (mod 2t-1k).

Original languageEnglish (US)
Pages (from-to)265-269
Number of pages5
JournalDiscrete Mathematics
Volume219
Issue number1-3
DOIs
StatePublished - May 28 2000

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Partition Function
Congruence
Dissection
Generating Function
Partition
Family

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Dolph, Laura L. ; Reynolds, Annmarie ; Sellers, James Allen. / Congruences for a restricted m-ary partition function. In: Discrete Mathematics. 2000 ; Vol. 219, No. 1-3. pp. 265-269.
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Dolph, LL, Reynolds, A & Sellers, JA 2000, 'Congruences for a restricted m-ary partition function', Discrete Mathematics, vol. 219, no. 1-3, pp. 265-269. https://doi.org/10.1016/S0012-365X(00)00024-8

Congruences for a restricted m-ary partition function. / Dolph, Laura L.; Reynolds, Annmarie; Sellers, James Allen.

In: Discrete Mathematics, Vol. 219, No. 1-3, 28.05.2000, p. 265-269.

Research output: Contribution to journalArticle

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