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，用于计算满足某些规定条件的对象的数量，例如集合、排列、矩阵……。在过去的几十年中，枚举组合学一直是数学研究中发展最快的领域之一，具有众多的联系和应用。该领域打破了传统的界限，与数学及其他领域的各个领域（从计算机科学到统计物理学）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。将研究的中心序列出现在枚举组合学中，涉及计数模式避免排列、遗传属性中的图以及凯莱图中的闭合游走。研究者将让各级学生参与他的研究。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值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: 2020-07
• 期刊: Mathematika
• 影响因子: 0.8
• 作者: Garber, Alexey;Pak, Igor
• 通讯作者: Pak, Igor