The covering number of a non-linear character $\chi$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $\chi^k$. We determine the covering numbers of irreducible characters of the symmetric group $S_n$ indexed by certain two-row partitions (and their conjugates), namely $(n-2,2)$, and $((n+1)/2, (n-1)/2)$ when $n$ is odd. We also determine the covering numbers of irreducible characters indexed by certain hook-partitions (and their conjugates), namely $(n-2,1^2)$, the almost self-conjugate hooks $(n/2+1, 1^{n/2-1})$ when $n$ is even, and the self-conjugate hooks $((n+1)/2, 1^{(n-1)/2})$ when $n$ is odd.
@article{10_37236_13289,
author = {Rijubrata Kundu and Velmurugan S},
title = {Covering numbers of some irreducible characters of the symmetric group},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13289},
zbl = {8062190},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13289/}
}
TY - JOUR
AU - Rijubrata Kundu
AU - Velmurugan S
TI - Covering numbers of some irreducible characters of the symmetric group
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/13289/
DO - 10.37236/13289
ID - 10_37236_13289
ER -
%0 Journal Article
%A Rijubrata Kundu
%A Velmurugan S
%T Covering numbers of some irreducible characters of the symmetric group
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/13289/
%R 10.37236/13289
%F 10_37236_13289
Rijubrata Kundu; Velmurugan S. Covering numbers of some irreducible characters of the symmetric group. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13289
