A. Miller

activity

20082025

most citedCongruences in character tables of symmetric groups

3 citations · 6 across the 14 of their papers we have counts for

collaborators

21 papers

math.RT2025

Denseness results for zeros and roots of unity in character tables

Alexander R. Miller

For any irreducible character $χ$ of a finite group $G$ , let $θ (χ)$ denote the proportion of elements $g \in G$ for which $χ (g)$ is either zero or a root of unity. Then for any $L\i…

math.GR2024

Short character values on large conjugacy classes

Alexander R. Miller

We provide an example of a finite group with a conjugacy class of average size on which fewer than half of the irreducible characters are either zero or a root of unity.

math.RT2023

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

Alexander R. Miller

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 char…

math.RT2023★ 1 cited

Large-scale Monte Carlo simulations for zeros in character tables of symmetric groups

Alexander R. Miller, Danny Scheinerman

This is a brief report on some recent large-scale Monte Carlo simulations for approximating the density of zeros in character tables of large symmetric groups. Previous computation…

math.RT2023★ 1 cited

Covering numbers for characters of symmetric groups

Alexander R. Miller

If $n > 4$ and $c (θ)$ denotes the set of irreducible constituents of a character $θ$ , then $c (χ^{k}) = Irr (S_{n})$ for all nonlinear $χ \in Irr (S_{n})$ if and only if $k \geq n - 1$ .

math.RT2021

The characters of symmetric groups that depend only on length

Alexander R. Miller

The characters $χ (π)$ of $S_{n}$ that depend only on the number of cycles of $π$ are completely determined.