From the 1 of 5 linked papers with an AI index.
5 papers
Universal Asymptotics and Exact Enumeration of Eulerian Maps
Ahmad Barhoumi, Roozbeh Gharakhloo, Nathan Hayford
The paper derives universal asymptotic formulas for counting labeled Eulerian maps of any genus with arbitrary degree sequences, and provides an exact enumeration for genus‑1 maps,…
The and Bi-orthogonal Polynomials on the Unit Circle: Further Properties and Riemann-Hilbert Characterizations
Roozbeh Gharakhloo, Nicholas S. Witte
In previous work \cite{GW}, we developed a theory of modulated \(2j-k\) bi-orthogonal polynomial systems \(\{P_n(z;r),Q_n(z;r)\}\) and \(j-2k\) bi-orthogonal polynomial systems \(\…
Reduction of Multiple Orthogonal Polynomials to Standard Orthogonal Polynomials
Roozbeh Gharakhloo, Maksim Kosmakov, Kenta Miyahara
In this article, we derive explicit formulae expressing multiple orthogonal polynomials in terms of standard orthogonal polynomials. We treat both the real-line and unit-circle set…
Combinatorics of Even-Valent Graphs on Riemann Surfaces
Roozbeh Gharakhloo, Tomas Lasic Latimer
In this paper, we derive explicit formulae for the number of regular even-valent graphs, with fixed minimal embedding genus, in which both the valence parameter and the number of v…
A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants II
Roozbeh Gharakhloo, Alexander Its
In this article, we continue the development of the Riemann-Hilbert formalism for studying the asymptotics of Toeplitz+Hankel determinants with non-identical symbols, which we init…