Covering numbers for characters of symmetric groups
Alexander R. Miller

TL;DR
This paper investigates the covering numbers of characters in symmetric groups, establishing conditions under which the set of irreducible constituents covers all irreducible characters for certain powers.
Contribution
It provides a characterization of when the irreducible constituents of character powers cover the entire set of irreducible characters in symmetric groups.
Findings
For $n>4$, the set of irreducible constituents of $ heta^k$ equals all irreducible characters iff $k \\geq n-1$.
The result applies to nonlinear irreducible characters of symmetric groups.
It advances understanding of the structure of character powers in symmetric groups.
Abstract
If and denotes the set of irreducible constituents of a character , then for all nonlinear if and only if .
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Graph theory and applications
