Geodesic
On a positivity conjecture in the character table of \(S_n\)
Sheila Sundaram1
1Pierrepont School
The electronic journal of combinatorics, Tome 26 (2019) no. 1

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Zbl arXiv
In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$ or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$ Many new Schur positivity questions are presented.
DOI : 10.37236/8186
Classification : 05E10, 05E18, 05A17, 11P81, 06A07, 20B30, 20C05, 20C15
Mots-clés : Schur positivity, character table, symmetric group

Sheila Sundaram  1

1 Pierrepont School 
Sheila Sundaram. On a positivity conjecture in the character table of \(S_n\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8186
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     author = {Sheila Sundaram},
     title = {On a positivity conjecture in the character table of {\(S_n\)}},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/8186},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/8186/}
}
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