Horizontal visibility graph of a random restricted growth sequence

TL;DR

This paper investigates the properties of horizontal visibility graphs derived from random restricted growth sequences and set partitions, providing formulas for expected node degrees involving Stirling and Bernoulli numbers.

Contribution

It introduces explicit formulas for expected degrees in horizontal visibility graphs based on combinatorial numbers, linking graph properties to classical number sequences.

Findings

Expected degree formulas involve Stirling and Bernoulli numbers

Provides explicit expressions for graph node degrees

Connects graph theory with combinatorial number sequences

Abstract

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and random set partitions of size $n.$ Our main results are formulas expressing the expected degree of graph nodes in terms of simple explicit functions of a finite collection of Stirling and Bernoulli numbers.