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Overcolored Partition Restricted by Parity of the Parts

M. P. Thejitha, S. N. Fathima

Abstract

Very recently, Thejitha, Sellers, and Fathima defined the function $a_{r,s}(n)$, which enumerates the number of multicolored partitions of $n$, wherein both even parts and odd parts may appear in one of $r$-colors and $s$-colors, respectively, for fixed $r,s\ge 1$. In this paper, we extend the concept to overpartitions.

Overcolored Partition Restricted by Parity of the Parts

Abstract

Very recently, Thejitha, Sellers, and Fathima defined the function , which enumerates the number of multicolored partitions of , wherein both even parts and odd parts may appear in one of -colors and -colors, respectively, for fixed . In this paper, we extend the concept to overpartitions.
Paper Structure (6 sections, 11 theorems, 58 equations)

This paper contains 6 sections, 11 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Preliminary Results
  3. Proof of Theorem \ref{['tmod4']}-\ref{['tmod8']}
  4. Congruences modulo powers of $2$
  5. Congruences modulo prime $p\ge 3$
  6. Concluding remark

Key Result

Theorem 1.1

For all $n\ge 1$,

Theorems & Definitions (19)

  • Theorem 1.1: das
  • Theorem 1.2: das
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Theorem 1.6
  • Theorem 1.7
  • Theorem 1.8
  • Lemma 2.1: poq
  • Lemma 2.2: tsf
  • ...and 9 more