双舒伯特多项式确实有饱和的牛顿多面体

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2023-11-03 DOI:10.1017/fms.2023.101

Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, Jonathan Montaño

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引用次数: 4

摘要

证明了二重舒伯特多项式具有饱和牛顿多面体性质。这解决了Monical, Tokcan和Yong的一个猜想。我们的想法是由多学位理论驱动的。我们引入了理想标准化的概念，使我们能够研究非标准多重评分。这使我们能够证明非标准乘法中每个Cohen-Macaulay素数理想的多次多项式的支持，特别是每个Schubert行列式理想的多次多项式的支持是一个离散的多矩阵。

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Double Schubert polynomials do have saturated Newton polytopes

We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ideal in a nonstandard multigrading, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid.

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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.