Mathematical Sciences: Research in Enumerative and AlgebraicCombinatorics

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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.