Work

Packing Density of Sets With Only Two Nonmixed Gaps

Year: 2025

Type: article

Abstract: ABSTRACT For a finite set of integers such that the first few gaps between its consecutive elements equal , while the remaining gaps equal , we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding optimal density, conjecture its tightness, and prove it in case one of the gap lengths, or , appears only once. This is equivalent to a Motzkin problem on the independence ratio of certain integer distance graphs.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.23269

Authors: Alexander Natalchenko, Arsenii Sagdeev

Institutions: Moscow Institute of Physics and Technology, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4411218641

FWCI:

Cites: 39

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Related to: 10