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 & Statistics

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

7 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

Bibliographical note

Funding Information:
The first author was supported by FAPESP (Grant no. 2016/14057-2). The authors thank the anonymous referee for his/her helpful comments and suggestions.

Publisher Copyright:
© 2019, Sociedade Brasileira de Matemática.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

Congruence
Designated summands
Generating function
Regular partition

Publisher link

10.1007/s00574-019-00156-x

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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 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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AU - Sellers, James A.

N1 - Funding Information: The first author was supported by FAPESP (Grant no. 2016/14057-2). The authors thank the anonymous referee for his/her helpful comments and suggestions. Publisher Copyright: © 2019, Sociedade Brasileira de Matemática. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

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.

KW - Congruence

KW - Designated summands

KW - Generating function

KW - Regular partition

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ER -

Infinitely Many Congruences for k-Regular Partitions with Designated Summands

Abstract

Bibliographical note

Keywords

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