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Incomplete perfect mendelsohn designs with block size 4 and one hole of size 7

✍ Scribed by F. E. Bennett; H. Shen; J. Yin

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
676 KB
Volume
1
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

Let v,k, and n be positive integers. An incomplete perfect Mendelsohn design, denoted by k‐IPMD__(v,n)__, is a triple (X, Y, 𝔹) where X is a v‐set (of points), Y is an n‐subset of X, and 𝔹 is a collection of cyclically ordered k‐subsets of X (called blocks) such that every ordered pair (a, b) ∈ (X Γ— X)βˆ–(Y Γ— Y) appears t‐apart in exactly one block of 𝔹 and no ordered pair (a,b) ∈ Y Γ— Y appears in any block of 𝔹 for any t, where 1 ≀ t ≀ k βˆ’ 1. In this article, we obtain conclusive results regarding the existence of 4‐IPMD(v,7) where the necessary conditions are v = 2 or 3(mod 4) and v β‰₯ 22. We also provide an application to the problem relating to coverings of PMDs with block size 4. Β© 1993 John Wiley & Sons, Inc.

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