5 citations · 5 across the 4 of their papers we have counts for
5 papers · 2 filters
Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior
Stephen Melczer, Mark C. Wilson
We consider the enumeration of walks on the non-negative lattice , with steps defined by a set . Previous…
Counting walks with large steps in an orthant
Alin Bostan, Mireille Bousquet-Mélou, Stephen Melczer
In the past fifteen years, the enumeration of lattice walks with steps takenin a prescribed set S and confined to a given cone, especially the firstquadrant of the plane, has been…
Counting partitions inside a rectangle
Stephen Melczer, Greta Panova, Robin Pemantle
We consider the number of partitions of whose Young diagrams fit inside an rectangle; equivalently, we study the coefficients of the -binomial coefficient $\…
Diagonal asymptotics for symmetric rational functions via ACSV
Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle +1
We consider asymptotics of power series coefficients of rational functions of the form where is a symmetric multilinear polynomial. We review a number of such cases from…
Vertically constrained Motzkin-like paths inspired by bobbin lace
Veronika Irvine, Stephen Melczer, Frank Ruskey
Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\se…