Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/26793
Title: | Minimizing the regularity of maximal regular antichains of 2- and 3-sets | Contributor(s): | Kalinowski, Thomas ; Leck, Uwe (author); Reiher, Christian (author); Roberts, Ian T (author) | Publication Date: | 2016-02 | Open Access: | Yes | Handle Link: | https://hdl.handle.net/1959.11/26793 | Open Access Link: | https://ajc.maths.uq.edu.au/pdf/64/ajc_v64_p277.pdf | Abstract: | Let n ≥ 3 be a natural number. We study the problem to find the smallest such that there is a family of 2-subsets and 3-subsets of [] = {1, 2, . . . ,} with the following properties: (1) is an antichain, i.e., no member of is a subset of any other member of ; (2) is maximal, i.e., for every ∈ 2⁽ⁿ⁾ \ there is an ∈ with ⊆ or ⊆ ; and (3) is -regular, i.e., every point ∈ [] is contained in exactly members of . We prove lower bounds on , and we describe constructions for regular maximal antichains with small regularity. | Publication Type: | Journal Article | Source of Publication: | Australasian Journal of Combinatorics, v.64, p. 277-288 | Publisher: | Centre for Discrete Mathematics & Computing | Place of Publication: | Australia | ISSN: | 2202-3518 1034-4942 |
Fields of Research (FoR) 2008: | 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Fields of Research (FoR) 2020: | 490404 Combinatorics and discrete mathematics (excl. physical combinatorics) | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article School of Science and Technology |
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