Complexity of Combinatorial Sequences

组合序列的复杂性

• 批准号: 1700444
• 负责人: Igor Pak
• 金额: $ 12万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700444&HistoricalAwards=false
• 关键词: Complexity; Combinatorial; Sequences

Enumerative combinatorics is the branch of mathematics that deals with counting the number of objects, such as sets, permutations, matrices,..., satisfying certain prescribed conditions. In the past several decades enumerative combinatorics has been one of the most rapidly developing areas of mathematical research, with numerous connections and applications. The area pushed away traditional boundaries and joined forces with a variety of fields in mathematics and beyond, ranging from computer science to statistical physics. The investigator will undertake a profound study of integer sequences using a broad and powerful range of mathematical tools. The central sequences that will be studied arise in enumerative combinatorics, involving counting pattern-avoiding permutations, graphs ina hereditary property, and closed walks in Cayley graphs. The investigator will involve students at all levels in his research.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.

枚举组合学是数学的一个分支，它处理对满足某些规定条件的对象的数量进行计数，如集合、排列、矩阵等。在过去的几十年里，列举组合学一直是数学研究中发展最快的领域之一，有着无数的联系和应用。该领域打破了传统的界限，与从计算机科学到统计物理等数学及其他领域的各个领域联手。研究人员将使用广泛而强大的数学工具对整数序列进行深入研究。将被研究的中心序列出现在计数组合学中，涉及计数模式避免排列、图的遗传性和Cayley图中的闭路。这位研究员将让所有级别的学生参与他的研究。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

CONCRETE POLYTOPES MAY NOT TILE THE SPACE

混凝土多面体可能无法铺满空间

• DOI: 10.1112/mtk.12052
• 发表时间: 2020
• 期刊: Mathematika
• 影响因子: 0.8
• 作者: Garber, Alexey;Pak, Igor
• 通讯作者: Pak, Igor