Algebraic combinatorics and
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.