Infinitely Many Congruences for k-Regular Partitions with Designated Summands

Robson da Silva; James A. Sellers

doi:10.1007/s00574-019-00156-x

Infinitely Many Congruences for k-Regular Partitions with Designated Summands

Robson da Silva, James A. Sellers

Mathematics

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

8 Scopus citations

Abstract

Andrews et al. (Acta Arith. 105:51–66, 2002) introduced and studied the partition function PD(n), the number of partitions of n with designated summands. Recently, congruences involving the number of ℓ-regular partitions with designated summands, denoted by PD_ℓ(n) , have been explored for specific fixed values of ℓ. In this paper, we provide several families containing infinitely many congruences for PD_k(n) for various values of k.

Original language	English (US)
Pages (from-to)	357-370
Number of pages	14
Journal	Bulletin of the Brazilian Mathematical Society
Volume	51
Issue number	2
DOIs	https://doi.org/10.1007/s00574-019-00156-x
State	Published - Jun 1 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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AB - Andrews et al. (Acta Arith. 105:51–66, 2002) introduced and studied the partition function PD(n), the number of partitions of n with designated summands. Recently, congruences involving the number of ℓ-regular partitions with designated summands, denoted by PDℓ(n) , have been explored for specific fixed values of ℓ. In this paper, we provide several families containing infinitely many congruences for PDk(n) for various values of k.

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Infinitely Many Congruences for k-Regular Partitions with Designated Summands

Abstract

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