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Bumpless pipedreams and Stanley symmetric functions

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时间:2018-09-06  来源:KLMM

题目:           Bumpless pipedreams and Stanley symmetric functions

报告人:      范久瑜博士 (四川大学数学学院)

时间地点:   2018.09.11  15:00pm  N109

摘要:           Thomas Lam, Seungjin Lee and Mark Shimozono (Back stable Schubert calculus, arXiv:1806.11233v1) introduced the structure of bumpless pipedreams. EG-pipedreams are a special kind of bumpless pipedreams. Lam, Lee and Shimozono posed the problem of finding a shape-preserving bijection between the set of EG-pipedreams of a permuation $w$ and the set of reduced word tableaux of $w$. In this talk, we present such a bijection. We first recall the definition and backgrounds of reduced word tableaux and bumpless pipedreams, including Coxeter-Knuth insertions, Lascoux-Schutzenberger trees, Little's bumping algorithm, Schubert polynomials and back stable Schubert polynomials. Then we introduce the modified Lascoux-Schutzenberger trees and EG-trees, which are the main structures of our bijection. Finally, we give a sketch of our bijection.

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