Algebraic combinatorics
Words and tableaux provide concrete ways to explore the structure of quasisymmetric functions and algebraic actions.
My interests center on quasisymmetric functions and the combinatorial objects that describe them. I am particularly interested in:
I study the expansion of Young quasisymmetric Schur functions into dual immaculate functions. A central part of this work is finding combinatorial explanations for cancellation in signed sums, using sign-reversing involutions on tableaux.
I investigate word encodings of tableaux and operators defined through matching rules. These models connect explicit combinatorial operations with 0-Hecke algebra actions and associated representations.
This project investigated the relationship between two families of quasisymmetric functions through combinatorial models.