完全对称自互补平面分区的烟斗梦视角

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-01-29 DOI:10.1017/fms.2023.131

Daoji Huang, Jessica Striker

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引用次数: 0

摘要

我们将完全对称自补平面分区（TSSCPP）描述为满足类似山内条件的有界相容序列。因此，它们与某些空想是双射的。利用这一特征和黄高最近提出的还原管状梦和还原无助管状梦之间的双射，我们给出了交替符号矩阵和 TSSCPP 在还原、1432 避开情况下的双射。我们还给出了 1432 避开和 2143 避开情况下的另一种偏射，它保留了相关梦幻泡影和无用梦幻泡影的自然正集结构。

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A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions

We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams. Using this characterization and the recent bijection of Gao–Huang between reduced pipe dreams and reduced bumpless pipe dreams, we give a bijection between alternating sign matrices and TSSCPP in the reduced, 1432-avoiding case. We also give a different bijection in the 1432- and 2143-avoiding case that preserves natural poset structures on the associated pipe dreams and bumpless pipe dreams.

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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.