Proofs of some conjectures of Keith and Zanello on t-regular partition

2022/01/18 by Singh, Ajit, Barman, Rupam
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.07046

Abstract

For a positive integer t, let b_t(n) denote the number of t-regular partitions of a nonnegative integer n. In a recent paper, Keith and Zanello established infinite families of congruences and self-similarity results modulo 2 for b_t(n) for certain values of t. Further, they proposed some conjectures on self-similarities of b_t(n) modulo 2 for certain values of t. In this paper, we prove their conjectures on b₃(n) and b₂₅(n). We also prove a self-similarity result for b₂₁(n) modulo 2.

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