# 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.

I currently serve on the editorial board of the journal Combinatorial Theory, which was formed by the majority of the JCTA editorial board in September 2020 as a mathematician-owned journal.

## Publications and preprints (in reverse chronological order)

- Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials (with Corteel, S, Haglund, J, Mandelshtam, O, and Williams, L), submitted for publication
- Lifting the Dual Immaculate functions (with Dominic Searles), submitted for publication
- Quasisymmetric Power Sums
(with Cristina Ballantine, Zajj Daugherty, Angela Hicks, and Elizabeth Niese), to appear in
*J. Combin. Theory Ser. A* - Recent trends in quasisymmetric functions, in Karaali, G., Orellana, R., eds.,
*Recent Trends in Algebraic Combinatorics*, Association for Women in Mathematics series, Springer, Cham, (2019): arXiv:2435046. - Dual immaculate quasisymmetric functions expand positively into Young quasisymmetric functions (with Ed Allen and Josh Hallam),
*J. Combin. Theory Ser. A*,**157**(2018), pp. 70-108. - Quasisymmetric $(k,l)$-hook Schur functions (with Elizabeth Niese),
*Ann. Comb.*,**22, no. 1**(2018), pp. 167-199. - Skew row-strict quasisymmetric Schur functions (with Elizabeth Niese),
*J. of Algebraic Combin.*,**42, no. 3**(2015), pp. 763-791. - 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.

by S K Mason.