2000 character limit reached
Using Graph Theory to Derive Inequalities for the Bell Numbers (2104.00552v2)
Published 1 Apr 2021 in cs.DM and math.CO
Abstract: The Bell numbers count the number of different ways to partition a set of $n$ 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.