Irreducible Symmetric Group Characters of Rectangular Shape
Richard P. Stanley
TL;DR
This paper introduces a new formula for calculating irreducible symmetric group characters for rectangular shapes, with observations and conjectures on extending to arbitrary shapes.
Contribution
It provides a novel formula for symmetric group characters of rectangular shape and explores potential generalizations.
Findings
New formula for rectangular shape characters
Observations on generalization to arbitrary shapes
Conjecture on extending the formula
Abstract
We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Finite Group Theory Research