Complexity of Combinatorial Sequences

枚举组合学是数学的分支，它处理对象的数量，如集合，排列，矩阵，.，满足一定的规定条件。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，有许多联系和应用。该领域打破了传统的界限，并与数学及其他领域的各种力量相结合，从计算机科学到统计物理学。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的研究。中心序列，将被研究出现在计数组合学，涉及计数模式，避免置换，图遗传性，并在凯莱图闭行走。该奖项反映了NSF的法定使命，并被认为是值得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的支持。

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.