On Some Identities of Barred Preferential Arrangements
Combinatorics
2015-04-07 v2
Abstract
A preferential arrangement of a finite set is an ordered partition. Associated with each such ordered partition is a chain of subsets or blocks endowed with a linear order. The chain may be split into sections by the introduction of a vertical bar, leading to the notion of a barred preferential arrangements. In this paper we derive some combinatorial identities satisfied by the number of possible barred preferential arrangements of an -element set. We illustrate with some suitable examples highlighting some important consequences of the identities.
Keywords
Cite
@article{arxiv.1503.06173,
title = {On Some Identities of Barred Preferential Arrangements},
author = {S. Nkonkobe and V. Murali},
journal= {arXiv preprint arXiv:1503.06173},
year = {2015}
}