24 citations · 78 across the 22 of their papers we have counts for
25 papers · 1 filter
Type multiline queues and the open-boundary TASEP
Olya Mandelshtam, Jerónimo Valencia-Porras
The totally asymmetric simple exclusion process (TASEP) with open boundaries is a finite Markov chain describing particles hopping between adjacent sites on a one-dimensional latti…
Shape changing identities for permuted-basement nonsymmetric Macdonald polynomials
Guilherme Zeus Dantas e Moura, Olya Mandelshtam
Permuted-basement Macdonald polynomials are nonsymmetric generalizations of symmetric Macdonald polynomials that form a basis for the polynomial ring $\math…
Bijections for rhombic alternative tableaux
Sylvie Corteel, Jang Soo Kim, Olya Mandelshtam +1
We generalize well-known bijections between alternative tableaux and permutations to bijections between rhombic alternative tableaux (RAT) and assemblées of permutations. We show h…
Positive expansions of permuted basement and quasisymmetric Macdonald polynomials at
Olya Mandelshtam, Harper Niergarth, Kartik Singh
It is well known that the -Whittaker polynomials, which are specializations of the Macdonald polynomials , expand positively as the sum of Schur polynomials. M…
New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
Olya Mandelshtam
We describe some recently discovered connections between one-dimensional interacting particle models and Macdonald polynomials. The first such model is the multispecies asymmetric…
Probabilistic Entry Swapping Bijections for Non-Attacking Fillings
Guilherme Zeus Dantas e Moura, Olya Mandelshtam
Non-attacking fillings are combinatorial objects central to the theory of Macdonald polynomials. A probabilistic bijection for partition-shaped non-attacking fillings was introduce…
Primeness of generalized parking functions
Sam Armon, Joanne Beckford, Dillon Hanson +4
Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any c…
Macdonald polynomials at t = 0 through twisted multiline queues
Olya Mandelshtam, Jerónimo Valencia-Porras
Multiline queues are versatile combinatorial objects that play a key role in understanding the remarkable connection between the asymmetric simple exclusion process (ASEP) on a cir…
Probabilistic operators for non-attacking tableaux and a compact formula for the symmetric Macdonald polynomials
Olya Mandelshtam
We prove a new tableaux formula for the symmetric Macdonald polynomials that has considerably fewer terms and simpler weights than previously existing formulas. Our fo…
Rhombic staircase tableaux and Koornwinder polynomials
Sylvie Corteel, Olya Mandelshtam, Lauren Williams
In this article we give a combinatorial formula for a certain class of Koornwinder polynomials, also known as Macdonald polynomials of type . In particular, we give a co…
Modified Macdonald polynomials and the multispecies zero range process: II
Arvind Ayyer, Olya Mandelshtam, James B. Martin
In a previous part of this work, we gave a new tableau formula for the modified Macdonald polynomials , using a weight on tableaux involving the \emph{queue…
Modified Macdonald polynomials and the multispecies zero range process: I
Arvind Ayyer, Olya Mandelshtam, James B. Martin
In this paper we prove a new combinatorial formula for the modified Macdonald polynomials , motivated by connections to the theory of interacting particle s…
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…
From multiline queues to Macdonald polynomials via the exclusion process
Sylvie Corteel, Olya Mandelshtam, Lauren Williams
Recently James Martin introduced multiline queues, and used them to give a combinatorial formula for the stationary distribution of the multispecies asymmetric simple exclusion exc…
Toric tableaux and the inhomogeneous two-species TASEP on a ring
Olya Mandelshtam
The inhomogeneous two-species TASEP on a ring is an exclusion process that describes particles of different species hopping clockwise on a ring with parameters giving the hopping r…
Rhombic alternative tableaux and assemblées of permutations
Olya Mandelshtam, Xavier Viennot
In this paper, we introduce the rhombic alternative tableaux, whose weight generating functions provide combinatorial formulae to compute the steady state probabilities of the two-…
Combinatorics of the two-species ASEP and Koornwinder moments
Sylvie Corteel, Olya Mandelshtam, Lauren Williams
In previous work, the first and third authors introduced staircase tableaux, which they used to give combinatorial formulas for the stationary distribution of the asymmetric simple…
Matrix ansatz and combinatorics of the -species PASEP
Olya Mandelshtam
We study a generalization of the partially asymmetric exclusion process (PASEP) in which there are species of particles of varying weights hopping right and left on a one-dimen…
Tableaux combinatorics of the two-species PASEP
Olya Mandelshtam, Xavier Viennot
We study a two-species PASEP, in which there are two types of particles, "heavy" and "light," hopping right and left on a one-dimensional lattice of cells with open boundaries.…
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…