کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4665010 | 1633782 | 2017 | 34 صفحه PDF | دانلود رایگان |
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.
Journal: Advances in Mathematics - Volume 306, 14 January 2017, Pages 89–122