Geodesic
On the divisibility of character values of the symmetric group
Jyotirmoy Ganguly1 ; Amritanshu Prasad2 ; Steven Spallone3
1Indian Institute of Science Education and Research
2The Institute of Mathematical Sciences
3Indian Institute of Science Education and Research, Pune
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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Fix a partition $\mu=(\mu_1,\dotsc,\mu_m)$ of an integer $k$ and positive integer $d$. For each $n>k$, let $\chi^\lambda_\mu$ denote the value of the irreducible character of $S_n$ at a permutation with cycle type $(\mu_1,\dotsc,\mu_m,1^{n-k})$. We show that the proportion of partitions $\lambda$ of $n$ such that $\chi^\lambda_\mu$ is divisible by $d$ approaches $1$ as $n$ approaches infinity.
DOI : 10.37236/8693
Classification : 20C30, 05A16, 05A17, 20C15
Mots-clés : symmetric group, character value, \(q\)-core tower

Jyotirmoy Ganguly  1   ; Amritanshu Prasad  2   ; Steven Spallone  3

1 Indian Institute of Science Education and Research
2 The Institute of Mathematical Sciences
3 Indian Institute of Science Education and Research, Pune 
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Jyotirmoy Ganguly; Amritanshu Prasad; Steven Spallone. On the divisibility of character values of the symmetric group. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8693

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