标题： 广义二项式系数的单调性与杰克正性 显示英文标题

标题： Monotonicity for generalized binomial coefficients and Jack positivity

摘要： 二项式公式对于舒尔多项式和杰克多项式由Lascoux在1978年研究过，以及在1990年代Kaneko，Okounkov--Olshanski和Lassalle。我们证明相关的二项式系数是单调的，并推导出一些对称函数不等式，特别是舒尔正性和杰克正性结果。这些不等式类似于牛顿，穆雷德，甘特迈赫，卡特勒--格林--斯坎德拉，斯拉和哈雷--陶所研究的。 显示英文摘要

摘要： Binomial formulas for Schur polynomials and Jack polynomials were studied by Lascoux in 1978, and Kaneko, Okounkov--Olshanski and Lassalle in the 1990s. We prove that the associated binomial coefficients are monotone and derive some symmetric function inequalities, in particular, a Schur positivity and Jack positivity result. These inequalities are similar to those studied by Newton, Muirhead, Gantmacher, Cuttler--Greene--Skandera, Sra and Khare--Tao.