Combinatorial Connections with Algebra, Geometry, Probability and Applications

与代数、几何、概率和应用的组合联系

基本信息

批准号：
1764012
负责人：
Sara Billey
金额：
$ 18.73万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1764012&HistoricalAwards=false
关键词：
Combinatorial Connections Algebra Geometry Probability

项目摘要

Combinatorics is an area of mathematics which is quintessential for applications in computer science, biology, physics, chemistry, and industry. Optimized algorithms based on combinatorics have revolutionized business decisions in our lifetime. Current research is uncovering connections to all areas of mathematics and science. This project focuses specifically on interdisciplinary applications of combinatorics in connection with problems in algebra,geometry, probability, and computer science. Combinatorial connections have been at the core of the investigator's prior work and continue to inspire innovation and collaboration. This project describes three main themes for research. The first relates to the classical study of the coinvariant algebra and its representation theory. The problem is to study the asymptotics of the underlying decomposition into irreducible symmetric group modules. The methods of attack include tools from combinatorics, algebra and probability theory. The second studies a newly proposed family of symmetric functions related to the matroid of 0-1 vectors in n-dimensional space. Conjectures and theorems in this direction use tools from algebraic geometry. This research has connections to physics and economics. The third topic, which is a mixture of combinatorics, theoretical computer science and discrete geometry, pertains to placements of circles in the plane with a wrapping condition. This area of research was inspired by the general discrete geometry problem of finding an appropriate polygonization of a region in the plane which appears in graphics and optimization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Combinatorics是数学领域，在计算机科学，生物学，物理，化学和工业中的应用是典型的应用。基于组合学的优化算法在我们的一生中彻底改变了业务决策。当前的研究正在发现与数学和科学所有领域的联系。该项目专门针对与代数，几何学，概率和计算机科学问题有关的组合学的跨学科应用。组合联系一直是调查员先前工作的核心，并继续激发创新与协作。该项目描述了研究三个主要主题。第一个涉及共同代数及其代表理论的经典研究。问题是研究基础分解为不可还原对称组模块的渐近学。攻击方法包括组合学，代数和概率理论的工具。第二个研究与N维空间中0-1载体的基曲线有关的新提出的对称函数系列。朝这个方向的猜想和定理使用代数几何形状的工具。这项研究与物理和经济学有联系。第三个主题是组合学，理论计算机科学和离散几何形状的混合物，与圆在平面中的位置有关。这一研究领域的灵感来自一般离散的几何问题，即在图形和优化中找到了飞机中某个区域的适当多边形化。该奖项反映了NSF的法定任务，并认为值得通过基金会的智力优点和更广泛的影响审查标准通过评估来进行评估。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A Pattern Avoidance Characterization for Smoothness of Positroid Varieties

正类品种平滑度的模式避免表征

DOI：
发表时间：
2022
期刊：
Séminaire lotharingien de combinatoire
影响因子：
0
作者：
Billey, Sara C.;Weaver, Jordan E.
通讯作者：
Weaver, Jordan E.

Asymptotic normality of the major index on standard tableaux

标准画面上主要指标的渐近正态性

DOI：
10.1016/j.aam.2019.101972
发表时间：
2020
期刊：
Advances in Applied Mathematics
影响因子：
1.1
作者：
Billey, Sara C.;Konvalinka, Matjaž;Swanson, Joshua P.
通讯作者：
Swanson, Joshua P.

Existence and Hardness of Conveyor Belts

输送带的存在与硬度

DOI：
10.37236/9782
发表时间：
2020
期刊：
The Electronic Journal of Combinatorics
影响因子：
0
作者：
Baird, Molly;Billey, Sara;Demaine, Erik;Demaine, Martin;Eppstein, David;Fekete, Sándor;Gordon, Graham;Griffin, Sean;Mitchell, Joseph;Swanson, Joshua
通讯作者：
Swanson, Joshua

The metric space of limit laws for $q$-hook formulas

$q$-hook 公式的极限定律的度量空间