Extensive parity analysis of broken 5-diamond partitions

Bernard L.S. Lin; Amita Malik; Andrew Y.Z. Wang

doi:10.1142/S1793042116500135

Extensive parity analysis of broken 5-diamond partitions

Bernard L.S. Lin, Amita Malik, Andrew Y.Z. Wang

Mathematics

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

1 Scopus citations

Abstract

In this paper, we investigate congruences for Δ5(n) modulo 2 and characterize the parity of Δ5(4n + 1) and Δ5(4n + 2) according to the arithmetic property of n. As a consequence, we obtain various Ramanujan type congruences for Δ5(n). We also extend these results to several infinite families of congruences.

Original language	English (US)
Pages (from-to)	219-236
Number of pages	18
Journal	International Journal of Number Theory
Volume	12
Issue number	1
DOIs	https://doi.org/10.1142/S1793042116500135
State	Published - Feb 1 2016

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042116500135

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abstract = "In this paper, we investigate congruences for Δ5(n) modulo 2 and characterize the parity of Δ5(4n + 1) and Δ5(4n + 2) according to the arithmetic property of n. As a consequence, we obtain various Ramanujan type congruences for Δ5(n). We also extend these results to several infinite families of congruences.",

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N2 - In this paper, we investigate congruences for Δ5(n) modulo 2 and characterize the parity of Δ5(4n + 1) and Δ5(4n + 2) according to the arithmetic property of n. As a consequence, we obtain various Ramanujan type congruences for Δ5(n). We also extend these results to several infinite families of congruences.

AB - In this paper, we investigate congruences for Δ5(n) modulo 2 and characterize the parity of Δ5(4n + 1) and Δ5(4n + 2) according to the arithmetic property of n. As a consequence, we obtain various Ramanujan type congruences for Δ5(n). We also extend these results to several infinite families of congruences.

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Extensive parity analysis of broken 5-diamond partitions

Abstract

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