English

An Exceptional Convolutional Recurrence

Combinatorics 2024-09-12 v2 Classical Analysis and ODEs History and Overview

Abstract

A quadratic recurrence of Faltung type, arising via ancestral path lengths of random binary trees, turns out to be related to the Painlev\'e I differential equation.

Keywords

Cite

@article{arxiv.2408.12440,
  title  = {An Exceptional Convolutional Recurrence},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:2408.12440},
  year   = {2024}
}

Comments

15 pages, 6 figures

R2 v1 2026-06-28T18:20:53.866Z