6 papers · 1 filter
Expanding the quasisymmetric Macdonald polynomials in the fundamental basis
Sylvie Corteel, Olya Mandelshtam, Austin Roberts
The quasisymmetic Macdonald polynomials were recently introduced by the first and second authors with Haglund, Mason, and Williams in [3] to refine the symmetric Mac…
Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
Sylvie Corteel, Jim Haglund, Olya Mandelshtam +2
We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynom…
Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
Sylvie Corteel, Jim Haglund, Olya Mandelshtam +2
We present several new and compact formulas for the modified and integral form of the Macdonald polynomials, building on the compact "multiline queue" formula for Macdonald polynom…
Cylindric rhombic tableaux and the two-species ASEP on a ring
Sylvie Corteel, Olya Mandelshtam, Lauren Williams
The asymmetric simple exclusion exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice of n sites. It was introduced around 1970, and since then has…
LGV proof of a determinantal theorem for TASEP probabilities
Olya Mandelshtam
The Totally Asymmetric Simple Exclusion Process (TASEP) is a non-equilibrium particle model on a finite one-dimensional lattice with open boundaries. In our earlier paper, we obtai…
Multi-Catalan Tableaux and the Two-Species TASEP
Olya Mandelshtam
The goal of this paper is to provide a combinatorial expression for the steady state probabilities of the two-species PASEP. In this model, there are two species of particles, one…