Emily Sergel

Research Interests

Algebraic combinatorics. I'm currently focusing on the combinatorics of Macdonald eigenoperators. This involves the following areas: parking functions, symmetric and quasi-symmetric functions, Macdonald polynomials, the space of diagonal harmonics, and others.

Papers

D. Qiu, J. Remmel, E. Sergel, and G. Xin. " On the Schur positivity of Δe2 en[X]." arXiv preprint arXiv:1710.03340.

J. Haglund and E. Sergel. " A generalized major index statistic on tableaux." arXiv preprint arXiv:1709.05996.

E. Sergel. " A proof of the Square Paths Conjecture." J. Comb. Theory, Series A 152C (2017) 363-379.

A. Garsia, E. Sergel Leven, N. Wallach, and G. Xin. " A new plethystic symmetric function operator and the rational shuffle conjecture at t=1/q." J. Comb. Theory, Series A 145 (2017) 57-100.

F. Bergeron, A. Garsia, E. Leven and G. Xin. "Some remarkable new plethystic operators in the theory of Macdonald polynomials." J. Comb. 7.4 (2016), 671-714.

F. Bergeron, A. Garsia, E. Leven and G. Xin. "Compositional (km,kn)-Shuffle Conjectures." Int. Math. Res. Not. (2015) rnr272.

T. Amdeberham and E. Leven. " Multi-cores, posets, and lattice paths." Adv. Appl. Math. 71 (2015), pp. 1-13.

A. Hicks and E. Leven. "A simpler formula for the number of diagonal inversions of an (m,n)-Parking Function and a returning Fermionic formula." Discrete Math. 383.3 (2015), pp. 48-65.

E. Leven. " Two special cases of the Rational Shuffle Conjecture." DMTCS FPSAC Proceedings (2014), pp. 789-800.

E. Leven, B. Rhoades and A. Wilson. "Bijections for the Shi and Ish Arrangements." European Journal of Combinatorics 39 (2014): 1-23.

A. Hicks and E. Leven. "A refinement of the Shuffle Conjecture with cars of two sizes and t=1/q." Journal of Combinatorics 5.1 (2014): 31-50.

P. Richter, E. Leven, A. Tran, B. Ek, J. Jacob, and D. Narayan "Rank numbers for bent ladders." Discussiones Mathematicae Graph Theory 34 (2014): 309-329.

E. Sergel. "Noncommutative Biorthogonal Polynomials." Advances in Applied Mathematics 48.1 (2012): 99-105.

E. Sergel, P. Richter, A. Tran, P. Curran, J. Jacob, and D. Narayan. "Rank numbers for some trees and unicyclic graphs." Aequationes Mathematicae 82.1-2 (2011): 65-79.