An explicit 1-factorization in the middle of the Boolean lattice
type: Item
instance of: scholarly article
title: An explicit 1-factorization in the middle of the Boolean lattice
zbMATH Open document ID: 0795.05111
DOI: 10.1016/0097-3165(94)90030-2
author: D. Duffus
author: H. A. Kierstead
author: Hunter Snevily
published in: Journal of Combinatorial Theory. Series A
publication date: 1994-09-07T00:00:00Z
review text: Let \(R_ j\) be the collection of \(j\)-element subsets of \(\{1,2, \dots, 2k+1\}\), and let \(B_ k\) be the bipartite graph defined on \(R_ k \cup R_{k+1}\) by letting \(A\) be adjacent to \(B\) if and only if \(A \subset B\) or vice versa. The authors define explicitly a 1-factorization of \(B_ k\) whose constituent matchings are defined using addition mod \(k+1\). They show that the matchings are invariant under rotation, they describe the effect of reflection, they show that there are no other symmetries that map these matchings among themselves, and they prove that they are distinct from the lexical matchings in \(B_ k\) (for lexical factorization see [\textit{H. A. Kierstead} and \textit{W. T. Trotter}, Explicit matchings in the middle levels of the Boolean lattice, Order 5, No. 2, 163-171 (1988; Zbl 0668.05045)]).
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 554407
zbMATH Keywords: Boolean lattice
zbMATH Keywords: 1-factorization
zbMATH Keywords: matchings
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90030-2
OpenAlex ID: W1982120981
cites work: Explicit matchings in the middle levels of the Boolean lattice
cites work: A sharp bound for the number of sets that pairwise intersect at \(k\) positive values
description: scientific article; zbMATH DE number 554407