Arithmetic Properties of Partitions with 1-colored Even Parts and r-colored Odd Parts

2025/09/29 by Thejitha, M. P., Fathima, S. N. · 2 citations
#05A17 (Primary) #11P83 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.24324

Abstract

Recently, Hirschhorn and Sellers defined the partition function a_r(n), which counts the number of partitions of n wherein even parts come in only one color, while the odd parts may appear in one of r-colors for fixed r≥1. The aim of this paper is to prove several new infinite families of congruences modulo 3 and 5 by employing a result of Newman and theory of modular forms.

Citations

• A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi--Colored Odd Parts
• A note on congruences for the difference between even cranks and odd cranks
• From crank to congruences

Cited by

• Congruences for generalized Color Partitions of Hirschhorn and Sellers
• Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima

Related

• A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi--Colored Odd Parts
• Congruences for generalized Color Partitions of Hirschhorn and Sellers
• Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima
• Congruence relations for r-colored partitions
• Some Observations on Modulo 5 Congruences for 2-Color Partitions