Minimizing the regularity of maximal regular antichains of 2- and 3-sets

Title: Minimizing the regularity of maximal regular antichains of 2- and 3-sets
Creator: Kalinowski, Thomas; Leck, Uwe; Reiher, Christian; Roberts, Ian T.
Relation: Australasian Journal of Combinatorics Vol. 64, Issue 2, p. 277-288
Relation: http://ajc.maths.uq.edu.au/?page=get_volumes&volume=64
Publisher: Centre for Discrete Mathematics & Computing
Resource Type: journal article
Date: 2016
Description: Let n ≥ 3 be a natural number. We study the problem of finding the smallest r such that there is a family Α of 2-subsets and 3-subsets of [n] = {1, 2,...,n} with the following properties: (1) Α is an antichain, i.e., no member of Α is a subset of any other member of A, (2) A is maximal, i.e., for every X ∈ 2^[n]\A there is an A ∈ A with X ⊆ A or A ⊆ X, and (3) A is r-regular, i.e., every point x ∈ [n] is contained in exactly r members of A. We prove lower bounds on r, and we describe constructions for regular maximal antichains with small regularity.
Subject: maximal regular antichains; lower bounds; 2- and 3-sets
Identifier: http://hdl.handle.net/1959.13/1320273
Identifier: uon:24113
Identifier: ISSN:1034-4942
Language: eng
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