Skewincidence

TL;DR

This paper introduces the concept of skewincidence between binary sequences, establishing bounds on the maximum size of sequence sets where each pair exhibits this property, bridging graph capacity and intersection problems.

Contribution

It defines skewincidence, a new relation between binary sequences, and derives sharp bounds on the maximum number of sequences with this property.

Findings

Established sharp bounds on sequence set sizes with skewincidence

Connected skewincidence to graph capacity and intersection problems

Provided theoretical framework for analyzing binary sequence relations

Abstract

We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1 or vice versa. We give rather sharp bounds on the maximum number of binary sequences of length n any pair of which has a skewincidence.