80 citations · 247 across the 15 of their papers we have counts for
15 papers
Weyl chambers for short step Quarter-plane Lattice Paths
Richard Brak
We consider four examples of short step lattice paths confined to the quarter plane. These are the Kreweras, Reverse Kreweras, Gessel, and Mishna-Rechnitzer lattice paths.The Rever…
Fibonacci, Motzkin, Schroder, Fuss-Catalan and other Combinatorial Structures: Universal and Embedded Bijections
R. Brak, N. Mahony
A combinatorial structure, , with counting sequence and ordinary generating function , is positive algebraic if…
Bi-orthogonal Polynomials and the Five parameter Asymmetric Simple Exclusion Process
R. Brak, W. Moore
We apply the bi-moment determinant method to compute a representation of the matrix product algebra -- a quadratic algebra satisfied by the operators and …
A Universal Bijection for Catalan Structures
Richard Brak
A Catalan magma is a unique factorisation normed magma with only one irreducible element. The \val partitions the base set into subsets enumerated by Catalan numbers. The primary t…
Bi-orthogonal Polynomial Sequences and the Asymmetric Simple Exclusion Process
Richard Brak, William Moore
We reformulate the Corteel-Williams equations for the stationary state of the two parameter Asymmetric Simple Exclusion Process (TASEP) as a linear map , ac…
Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions
Richard Brak, John Essam
We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the rep…