Journal of Integer Sequences, Vol. 23 (2020), Article 20.2.3

The Minimal Excludant in Integer Partitions

George E. Andrews
The Pennsylvania State University
University Park, PA 16802

David Newman
Far Rockaway, New York


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.

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(Concerned with sequences A027187 A046682 A064428 A260894.)

Received February 24 2019; revised versions received July 24 2019; October 26 2019; October 30 2019; February 16 2020. Published in Journal of Integer Sequences, February 17 2020.

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