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

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.

8 pages, title and introduction updated, comments are welcome