The minimal excludant in integer partitions

The minimal excludant, or “mex” function, on a set S of positive integers is the least positive integer not in S. In this paper, the mex function is extended to integer partitionsgeneralizedbyconstrictingtheuniversalsetfromallpositiveintegerstothose in certain arithmetic progressions. There are numerous surprising partition identities connected with this restricted mex function. This paper provides an account of some of the most conspicuous cases.