Divisibility of Certain Partition Functions and Modular Forms

Abstract

This thesis studies arithmetic properties of certain partition functions namely mexrelated partition functions Andrews singular overpartitions tregular partitions and 3regular color partitions Firstly we study the mexrelated partition function which has been introduced by Andrews and Newman very recently The minimal excludant or mex function on a set S of positive integers is the least positive integer not in S Andrews and Newman extended the mexfunction to integer partiti