# 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), submitted for publication
- Row-strict quasisymmetric Schur functions (with Jeff Remmel),
*Annals of Combinatorics*, to appear (2012). - A graph theoretical approach to solving Scramble Squares puzzles (with Mali Zhang),
*Involve*, to appear (2012). - Properties of the nonsymmetric Robinson-Schensted-Knuth algorithm (with James Haglund and Jeff Remmel), submitted for publication (2011).
- 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.

## Recent and upcoming presentations

- AMS Spring Eastern Sectional Meeting, Washington, DC (March 17-18, 2012).
- AMS Spring Southeastern Sectional Meeting, Tampa, Florida (March 10-11, 2012).
- FPSAC: Formal Power series and algebraic combinatorics conference, Reykjavik, Iceland (June 13-17, 2011).
- Banff International Research Station Algebraic Combinatorixx workshop , Banff, Canada (May 22-27, 2011)
- Special Session on Combinatorial Representation Theory, AMS Spring Eastern Section Meeting, Worcester, MA (April 9-10, 2011).
- Special Session on Algebraic and Enumerative Combinatorics, AMS Spring Southeastern Section Meeting, Statesboro, GA (March 12-13, 2011).
- Banff International Research Station Workshop on quasisymmetric functions, Banff, Canada (November 14-19, 2010).
- FPSAC: Formal Power series and algebraic combinatorics conference, San Francisco, CA (August 2-6, 2010).
- Special Session on Partition Theory and the combinatorics of symmetric functions, AMS Spring Central Section Meeting, St. Paul, MN (April 10-11, 2010).
- UBC Combinatorics Seminar, Vancouver, BC (April 13, 2010).
- AMS Special Session on Enumerative Combinatorics, Joint Mathematics Meetings, San Francisco, CA (January 15, 2010).

by S K Mason.