Crystal Chute Moves on Pipe Dreams

IF 0.8 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2025-03-12 DOI:10.1007/s00026-025-00747-0

Sarah Gold, Elizabeth Milićević, Yuxuan Sun

引用次数: 0

Abstract

Schubert polynomials represent a basis for the cohomology of the complete flag variety and thus play a central role in geometry and combinatorics. In this context, Schubert polynomials are generating functions over various combinatorial objects, such as rc-graphs or reduced pipe dreams. By restricting Bergeron and Billey’s chute moves on rc-graphs, we define a Demazure crystal structure on the monomials of a Schubert polynomial. As a consequence, we provide a method for decomposing Schubert polynomials as sums of key polynomials, complementing related work of Assaf and Schilling via reduced factorizations with cutoff, as well as Lenart’s coplactic operators on biwords.

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水晶滑道移动管道梦想

舒伯特多项式是完全旗种上同调的基础，在几何学和组合学中占有重要地位。在这种情况下，舒伯特多项式在各种组合对象上生成函数，比如rc图或简化的白日梦。通过在rc图上限制Bergeron和Billey的溜槽运动，我们在舒伯特多项式的单项式上定义了一个Demazure晶体结构。因此，我们提供了一种将Schubert多项式分解为关键多项式和的方法，补充了Assaf和Schilling通过带截断的约简因式分解的相关工作，以及Lenart在双字上的共积算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches