New Congruences for $2$-Color Partitions and $t$-Core Partitions

S. N. Fathima; Utpal Pore; M. A. Sriraj; P. Siva Kota Reddy

doi:10.5269/bspm.70916

S. N. Fathima Pondicherry University
Utpal Pore St. Xavier's University
M. A. Sriraj Vidyavardhaka College of Engineering, Mysuru, India
P. Siva Kota Reddy JSS Science and Technology University, Mysuru, India

Abstract

Let $c_N(n)$ denote the number of $2$-color partition of $n$ subject to the restriction that one of the colors appears only in parts that are divisible by $N$. If $t$ is a positive integer, then a partition of a nonnegative integer $n$ is a $t$-core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of $t$. Let $a_t(n)$ denote the number of $t$-core partitions of $n$. In this paper, we obtain new congruences modulo $3$ for the $2$-color partition function $c_{11}(n)$, $t$-core partition functions $a_5(n)$ and $a_{11}(n)$.

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Author Biographies

S. N. Fathima, Pondicherry University

Associate Professor of Mathematics

Utpal Pore, St. Xavier's University

Assistant Professor of Mathematics

M. A. Sriraj, Vidyavardhaka College of Engineering, Mysuru, India

Associate Professor of Mathematics

P. Siva Kota Reddy, JSS Science and Technology University, Mysuru, India

Professor and Head, Department of Mathematics

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