On a positivity conjecture in the character table of $S_n$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916938134847488 |
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| author | Sundaram, Sheila |
| author_facet | Sundaram, Sheila |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_01416 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On a positivity conjecture in the character table of $S_n$ Sundaram, Sheila Combinatorics Group Theory 05E18, 20C05 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. |
| title | On a positivity conjecture in the character table of $S_n$ |
| topic | Combinatorics Group Theory 05E18, 20C05 |
| url | https://arxiv.org/abs/1808.01416 |