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} }
In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.
6 Citations
On even entries in the character table of the symmetric group
- Mathematics
- 2020
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…
Divisibility of character values of the symmetric group by prime powers
- 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.
Almost all entries in the character table of the symmetric group are multiples of any given prime
- MathematicsJournal 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.
Nonsolvable Groups have a Large Proportion of Vanishing Elements
- MathematicsIsrael Journal of Mathematics
- 2022
Groups with a small average number of zeros in the character table
- MathematicsJournal of Algebra
- 2022
Zeros and roots of unity in character tables
- Mathematics
- 2020
. 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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