Matrix Representations From Labeled Trees
Charlie Liou and Anthony Mendes
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA 93407
USA
Abstract:
Let X be the matrix representation induced by the action of the symmetric
group on labeled trees with n vertices. We show that the number of times
that the irreducible representation of the symmetric group corresponding
to the integer partition (n – 1, 1) appears within X
is the number of unlabeled trees with certain conditions.
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(Concerned with sequences
A000272
A217420.)
Received May 18 2023; revised version received August 14 2023.
Published in Journal of Integer Sequences,
August 15 2023.
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