Using Graph Theory to Derive Inequalities for the Bell Numbers
Discrete Mathematics
2024-03-11 v2 Combinatorics
Abstract
The Bell numbers count the number of different ways to partition a set of elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach.
Keywords
Cite
@article{arxiv.2104.00552,
title = {Using Graph Theory to Derive Inequalities for the Bell Numbers},
author = {Alain Hertz and Anaelle Hertz and Hadrien Mélot},
journal= {arXiv preprint arXiv:2104.00552},
year = {2024}
}