关于Jack多项式的Schur展开的一些猜想

IF 0.4 Q4 MATHEMATICS, APPLIED Journal of Combinatorics Pub Date : 2018-10-26 DOI:10.4310/joc.2021.v12.n2.a2

P. Alexandersson, J. Haglund, George Wang

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引用次数: 2

摘要

给出了二项式系数给出的两基中Jack对称函数的Schur展开式的正猜想。部分结果表明，在这些基中存在丰富的组合，包括欧拉数、斯特林数、拟山内图和车棋盘。这些结果还导致了关于这些基的基本准对称展开的进一步猜想，我们在特殊情况下证明了这些猜想。

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Some conjectures on the Schur expansion of Jack polynomials

We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.

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Journal of Combinatorics MATHEMATICS, APPLIED-

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