标题： Schubert多项式，滑动多项式，Stanley对称函数和拟Yamanouchi管道图 显示英文标题

标题： Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams

摘要： 我们引入了多项式中的两个新基底，它们将单项函数和基本拟对称函数提升到整个多项式环中。通过定义管道图的一种新条件，称为拟山ノ内条件，我们给出了一个正组合规则，用于将Schubert多项式展开到这些新基底上，这与Schur函数在基本拟对称函数上的展开相平行。由此，我们得到了Schubert多项式的稳定极限向Stanley对称函数的细化。我们还给出了这些基底的正结构常数的组合规则，它们分别推广了拟shuffle积和shuffle积。我们用此来给出将Schubert多项式乘积展开为基本滑动多项式的Littlewood--Richardson法则，并给出Stanley对称函数乘积在Schubert结构常数方面的公式。 显示英文摘要

摘要： We introduce two new bases for polynomials that lift monomial and fundamental quasisymmetric functions to the full polynomial ring. By defining a new condition on pipe dreams, called quasi-Yamanouchi, we give a positive combinatorial rule for expanding Schubert polynomials into these new bases that parallels the expansion of Schur functions into fundamental quasisymmetric functions. As a result, we obtain a refinement of the stable limits of Schubert polynomials to Stanley symmetric functions. We also give combinatorial rules for the positive structure constants of these bases that generalize the quasi-shuffle product and shuffle product, respectively. We use this to give a Littlewood--Richardson rule for expanding a product of Schubert polynomials into fundamental slide polynomials and to give formulas for products of Stanley symmetric functions in terms of Schubert structure constants.