80 citations · 685 across the 76 of their papers we have counts for
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Area and water-capacity statistics for upper hulls of Dyck paths
Aleksander L. Owczarek, Thomas Prellberg
We study Dyck paths refined simultaneously by proper area and water capacity, where water capacity is measured above the path and below its lattice-path upper hull. The finite-heig…
Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models
Nicholas R. Beaton, Aleksander L. Owczarek, Ruijie Xu
Lattice paths in the quarter plane have led to a large and varied set of results in recent years. One major project has been the classification of step sets according to the proper…
Exact solution of some quarter plane walks with interacting boundaries
Nicholas R Beaton, Aleksander L Owczarek, Andrew Rechnitzer
The set of random walks with different step sets (of short steps) in the quarter plane has provided a rich set of models that have profoundly different integrability properties. In…
Enumeration of area-weighed Dyck paths with restricted height
Aleksander L Owczarek, Thomas Prellberg
We derive explicit expressions for -orthogonal polynomials arising in the enumeration of area-weighted Dyck paths with restricted height.
From the Bethe Ansatz to the Gessel-Viennot Theorem
R. Brak, J. W. Essam, A. L. Owczarek
We state and prove several theorems that demonstrate how the coordinate Bethe Ansatz for the eigenvectors of suitable transfer matrices of a generalised inhomogeneous five-vertex m…