Revisiting the spreading and covering numbers

TL;DR

This paper explores the properties of spreading and covering numbers, establishing new connections and algorithms to improve bounds, advancing understanding in combinatorial mathematics.

Contribution

It introduces a novel link between spreading numbers and non-negative integer matrices, and develops an algorithm for tighter upper bounds on covering numbers.

Findings

Established a connection between spreading numbers and 2x2 matrices with sum d

Developed an algorithm for improved upper bounds on covering numbers

Provided new insights into the computation of these combinatorial quantities

Abstract

We revisit the problem of computing the spreading and covering numbers. We show a connection between some of the spreading numbers and the number of non-negative integer 2x2 matrices whose entries sum to d, and we construct an algorithm to compute improved upper bounds for the covering numbers.