Using Periodicity to Obtain Partition Congruences

2016/09/12 by Ali H. Al-Saedi, Al-Saedi, Ali H.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1609.03633

openalex publication_date 2016/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial functions based on a bounded number of calculations. As applications of our result, we establish new and existing restricted plane partition congruences, restricted plane overpartition congruences and several examples of restricted partition congruences.

Citations

• Dyson’s ranks and Maass forms

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