Unimodality conjecture for skew standard Young tableau distributions

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Let λ\lambda and μ\mu be partitions with μ⊆λ\mu\subseteq\lambda, and let fλ∖μ,i(q)f_{\lambda\setminus\mu,i}(q) denote the major-index generating polynomial for standard Young tableaux of skew shape λ∖μ\lambda\setminus\mu having ii descents. Skew-tableau unimodality conjecture. The polynomials fλ∖μ,i(q)f_{\lambda\setminus\mu,i}(q) are unimodal.

This conjecture seeks to extend known unimodality results for major-index distributions from ordinary to skew standard Young tableaux. The supplied text gives no resolution status.

References

Primary source

William J. Keith, “Families of major index distributions: closed forms and unimodality”, arXiv:1808.01362 (2018).

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