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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 partitions generalized by constricting the universal set from all positive integers to those 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.