Mathematical Sciences: Research in Enumerative and AlgebraicCombinatorics

本文主要研究部分有序集合的组合性质，特别是Coxeter群上的Bruhat序和弱序的性质。对于对称群，我们将探讨有关排列统计、弱序和偏序集的线性扩展的几个问题。组合数学是关于有限集的各种问题的研究。这些问题贯穿于整个数学领域，在计算机科学、实验设计和编码理论等领域都有重要的应用。

This research is in enumerative and algebraic combinatorics, and focuses on combinatorial properties of partially ordered sets, particularly on properties of Bruhat order and weak order on Coxeter groups. For the symmetric group, several questions dealing with permutation statistics, weak order, and linear extensions of posets will be explored. Combinatorial mathematics is the study of various problems concerning finite sets. Such problems arise throughout mathematics, and have important applications to such fields as computer science, design of experments, and coding theory.