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Journal Article
Partitions and the Minimal Excludant
2019
Overview
Fraenkel and Peled have defined the minimal excludant or “
mex
” function on a set
S
of positive integers is the least positive integer not in
S
. For each integer partition
π
, we define
mex
(
π
)
to be the least positive integer that is not a part of
π
. Define
σ
mex
(
n
)
to be the sum of
mex
(
π
)
taken over all partitions of
n
. It will be shown that
σ
mex
(
n
)
is equal to the number of partitions of
n
into distinct parts with two colors. Finally the number of partitions
π
of
n
with
mex
(
π
)
odd is almost always even.
Publisher
Springer International Publishing,Springer Nature B.V
