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- W23533958 abstract "Abstract An imbrical design is a minimal, but not necessarily minimum, covering. Thus, a pair (V,D) is an ID (u,k,λ,b) if and only if (a) |V|=v (b) D is a collection of b k -subsets of V called blocks (c) every pair of elements of V is in at least λ blocks (d) for every b ∈ D there is a pair {x,y}⊂b so that λ is in exactly X blocks ({x,y} is called essential for b ) (d') equivalently, if D'dD, (V,D') is not an imbrical design. Given v, k , and λ, the spectrum Spec(v,k,λ) = { b :there exists ID (u,k,λ,b)}. In this paper we determine Spec (v, 3,1) for all v and Spec (u,4,1) except for (v,b) , where v ∈{25,28,37,40,85}, b = . The results are that min Spec(v, 3,1)= max 5pec(v,3,1) = and that Spec{v,3,1) is an interval except that v=3 , 6=2 and v=7 , 6=8 do not exist. For k=4 we have similar results: min Spec(v ,4,1) = max Spec(v ,4,1) = and Spec(v,4,1) is an interval except possibly for the noted values, and v=4, b =2, v =13, b =14 do not exist." @default.
- W23533958 created "2016-06-24" @default.
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- W23533958 date "1987-01-01" @default.
- W23533958 modified "2023-09-26" @default.
- W23533958 title "On the Spectrum of Imbrical Designs" @default.
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- W23533958 doi "https://doi.org/10.1016/s0304-0208(08)72902-5" @default.
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