Interassociates of the Free Commutative Semigroup on n Generators |
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Authors: | Berit Nilsen Givens Karen Linton Amber Rosin Laurie Dishman |
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Institution: | (1) Cal Poly Pomona, 3801 W. Temple Ave., Pomona, CA 91768, USA;(2) Cumberland University, One Cumberland Square, Lebanon, TN 37087, USA |
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Abstract: | The interassociates of the free commutative semigroup on n generators, for n > 1, are identified. For fixed n, let (S, ·)
denote this semigroup. We show that every interassociate can be written in the form
, depending only on a n-tuple
. Next, if
and
are isomorphic interassociates of (S, ·) such that
, for xii and xj in the generating set of S, then
. Moreover,
if and only if
is a permutation of
. |
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Keywords: | |
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