Congruences modulo powers of $2$ for three restricted partition functions of Pushpa and Vasuki

TL;DR

This paper proves infinite families of congruences modulo powers of 2 for three specific restricted partition functions, expanding on recent results using elementary q-series methods.

Contribution

It introduces new infinite families of congruences for three restricted partition functions, generalizing recent specific congruences through elementary techniques.

Findings

Established infinite families of 2-adic congruences

Generalized recent specific congruences

Applied elementary q-series methods

Abstract

We establish infinite families of congruences modulo arbitrary powers of $2$ for the three restricted partition functions $M(n), T^\ast(n)$, and $P^\ast(n)$ introduced by Pushpa and Vasuki by employing elementary $q$-series techniques. These generalize some particular congruences for $M(n), T^\ast(n)$, and $P^\ast(n)$ recently found by Nath and Saikia.