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Character and class parameters from entries of character tables of symmetric groups

Part of: Representation theory of groups

Published online by Cambridge University Press:  05 June 2025

ALEXANDER ROSSI MILLER
ALEXANDER ROSSI MILLER*
Affiliation:
Center for Communications Research, Princeton e-mail: a.miller@ccr-princeton.org
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Abstract

If all of the entries of a large $S_n$ character table are covered up and you are allowed to uncover one entry at a time, then how can you quickly identify all of the indexing characters and conjugacy classes? We present a fast algorithmic solution that works even when n is so large that almost none of the entries of the character table can be computed. The fraction of the character table that needs to be uncovered is $O( n^2 \exp({-}2\pi\sqrt{n/6}))$, and for many of these entries we are only interested in whether the entry is zero.

MSC classification

Primary: 20C30: Representations of finite symmetric groups
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , First View , pp. 1 - 9
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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