Intervals of Antichains and Their Decompositions
Combinatorics
2016-02-16 v1
Abstract
An antichain of subsets is a set of subsets such that no subset in the antichain is a proper subset of any other subset in the antichain. The Dedekind number counts the total number of antichains of subsets of an n-element set. This paper investigates the interval structure of the lattice of antichains. Several partitioning theorems and counting formulas for the size of intervals are derived.
Keywords
Cite
@article{arxiv.1602.04675,
title = {Intervals of Antichains and Their Decompositions},
author = {Patrick De Causmaecker and Stefan De Wannemacker and Jay Yellen},
journal= {arXiv preprint arXiv:1602.04675},
year = {2016}
}
Comments
31pages