5 citations · 5 across the 2 of their papers we have counts for
11 papers · 1 filter
Homotopy techniques for analytic combinatorics in several variables
Kisun Lee, Stephen Melczer, Josip Smolčić
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the…
Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes
Stephen Melczer, Marc Mezzarobba
We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. The proof builds on a result of Yu and Chen that reduces…
Asymptotic bounds on graphical partitions and partition comparability
Stephen Melczer, Marcus Michelen, Somabha Mukherjee
An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size is graphical de…
Asymptotic enumeration of lonesum matrices
Jessica Khera, Erik Lundberg, Stephen Melczer
We provide bivariate asymptotics for the poly-Bernoulli numbers, a combinatorial array that enumerates lonesum matrices, using the methods of Analytic Combinatorics in Several Vari…
Stationary points at infinity for analytic combinatorics
Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key t…
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…