Locally Restricted Sequential Structures and Runs of a Subcomposition in Integer Compositions

TL;DR

This paper investigates the distribution of part sizes in supercritical locally restricted sequential structures, extending previous work on integer compositions and applying transfer matrix methods to analyze runs of subcompositions.

Contribution

It introduces a generalized framework for analyzing part sizes in locally restricted structures and applies infinite digraph enumeration techniques to study subcomposition runs.

Findings

Extended results to supercritical locally restricted structures

Connected part size distributions to infinite digraph enumeration

Provided applications for runs of subcompositions in compositions

Abstract

We study part sizes of supercritical locally restricted sequential structures. This extends previous results about locally restricted integer compositions and part sizes in smooth supercritical compositional structures. Applications are given for runs of subcompositions. The problems are formulated as enumerating directed walks in sized infinite digraphs and the proofs depend heavily on earlier results by Bender and Canfield about infinite transfer matrices.