An Exceptional Convolutional Recurrence
Steven Finch
TL;DR
This paper explores a quadratic recurrence relation derived from ancestral path lengths in random binary trees, revealing its connection to the Painlevé I differential equation, thus linking combinatorial structures with complex differential equations.
Contribution
It introduces a novel recurrence relation based on binary tree structures and establishes its relation to the Painlevé I equation, bridging combinatorics and differential equations.
Findings
Recurrence relates to ancestral path lengths in binary trees
Connection established with Painlevé I differential equation
Provides new insights into combinatorial and differential equation links
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.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Geometry and complex manifolds · Polynomial and algebraic computation