Combinatorics of higher order degenerate r-deranged bell numbers with singletons
General Mathematics
2026-05-12 v1
Abstract
When one inserts a number of identical bars in between blocks of an ordered set partition, they get a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred preferential arrangements with no fixed blocks, and ones where the first r elements of a set are singletons. We derive several combinatorial identities. Combinatorially these numbers are a kind of generalized barred preferential arrangements. We also provide some asymptotic results for these numbers.
Keywords
Cite
@article{arxiv.2605.08304,
title = {Combinatorics of higher order degenerate r-deranged bell numbers with singletons},
author = {Sithembele Nkonkobe},
journal= {arXiv preprint arXiv:2605.08304},
year = {2026}
}