The sparsity of character tables of high rank groups of Lie type

@article{Larsen2020TheSO,
title={The sparsity of character tables of high rank groups of Lie type},
author={Michael Larsen and Alexander R. Miller},
journal={Representation Theory of the American Mathematical Society},
year={2020}
}
• Published 1 June 2020
• Mathematics
• Representation Theory of the American Mathematical Society
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.
We show that almost every entry in the character table of $S_n$ is even as $n\to\infty$. This resolves a conjecture of Miller. We similarly prove that almost every entry in the character table of
• Mathematics
• 2023
. Let k be a positive integer. We show that, as n goes to inﬁnity, almost every entry of the character table of S n is divisible by k . This proves a conjecture of Miller.
• Mathematics
Journal für die reine und angewandte Mathematik (Crelles Journal)
• 2022
Abstract We show that almost every entry in the character table of S N {S_{N}} is divisible by any fixed prime as N → ∞ {N\to\infty} . This proves a conjecture of Miller.
. For any ﬁnite group G , Thompson proved that, for each χ ∈ Irr( G ), χ ( g ) is a root of unity or zero for more than a third of the elements g ∈ G , and Gallagher proved that, for each larger than

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