Linear chord diagrams with long chords
Everett Sullivan

TL;DR
This paper studies linear chord diagrams with long chords, revealing that the counts along diagonals follow a geometric sequence and identifying when this pattern begins.
Contribution
It proves that the geometric sequence pattern holds for all diagonals in linear chord diagrams with long chords and determines the onset of this pattern.
Findings
Diagonal counts follow a geometric sequence
Pattern holds for all diagonals
Identifies when the geometric pattern starts
Abstract
A linear chord diagram of size is a partition of the set into sets of size two, called chords. From a table showing the number of linear chord diagrams of degree such that every chord has length at least , we observe that if we proceed far enough along the diagonals, they are given by a geometric sequence. We prove that this holds for all diagonals, and identify when the effect starts.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · semigroups and automata theory
