# Algebraic combinatorics and

representation theory

My main research focus is on specializations of Macdonald polynomials. In particular, I am interested in the combinatorial properties of families of polynomials that can by constructed using diagrams such as Young tableaux. For more details about my research, please see my research statement (last updated in the fall of 2008).

## Publications and preprints (in reverse chronological order)

- A geometric and combinatorial view of weighted voting (with Jason Parsley), pre-print
- Quasisymmetric (k,l)-hook Schur functions (with Elizabeth Niese), submitted for publication
- Skew row-strict quasisymmetric Schur functions (with Elizabeth Niese), to appear in
*J. of Algebraic Combin.* - Row-strict quasisymmetric Schur functions (with Jeff Remmel),
*Annals of Combinatorics*,**18**(2014), pp. 127-148. - Properties of the nonsymmetric Robinson-Schensted-Knuth algorithm (with James Haglund and Jeff Remmel),
*J. of Algebraic Combin.*,**38, no. 2**(2013), pp. 285-327. - A graph theoretical approach to solving Scramble Squares puzzles (with Mali Zhang),
*Involve*,**5, no. 3**(2012), pp. 313-325. - Qsym over Sym has a stable basis (with Aaron Lauve),
*J. Combin. Theory Ser. A*,**118**, (2011), pp. 1661-1673. - Refinements of the Littlewood-Richardson Rule (with James Haglund, Kurt Luoto, and Steph van Willigenburg),
*Trans. Amer. Math. Soc.*,**363**(2011), pp. 1665-1686. - Quasisymmetric Schur functions (with James Haglund, Kurt Luoto, and Steph van Willigenburg),
*J. Combin. Theory Ser. A*,**118**, (2011), pp. 463-490. - An explicit construction of type A Demazure atoms,
*J. Algebraic Combin.***23**(2009) , pp. 295-313. - A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm,
*Seminaire Lotharingien de Combinatoire Article***B57e**(2008), 24pp.

## Slides from ECCO 2016

Geometric and Combinatorial Weighted Voting: Some Open Problemsby S K Mason.