# 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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