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arXiv · 1808.01416

On a positivity conjecture in the character table of $S_n$

Sheila Sundaram
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Abstract

In previous work of this author it was conjectured that the sum of power sums $p_λ,$ for partitions $λ$ ranging over an interval $[(1^n), μ]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $μ\in [(n-4,1^4), (n)]$ or $μ\in [(1^n), (3,1^{n-3})], $ or $μ=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$ Many new Schur positivity questions are presented.

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Sheila Sundaram. 2018-12-21. On a positivity conjecture in the character table of $S_n$. https://doi.org/10.37236/8186

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