The Minimal Excludant in Integer Partitions
George E. Andrews
The Pennsylvania State University
University Park, PA 16802
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.
Full version: pdf,
(Concerned with sequences
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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