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We illustrate our approach with an application in the design of order picking warehouses.
For each n≡0 or 1 (mod 8), we determine the spectrum of all the integers v such that there is a nontrivial handcuffed design of order v and block size s embedded in a D-design of order n.
Also solved is the more general problem of finding necessary and sufficient conditions for the embedding of a partial 3-path design of order n into a 3-path design of order k≥n+2.
In this paper, necessary and sufficient conditions are found for embedding a maximal partial 3-path design of order n into a 3-path design of specified order.
Let (X,B) be a λ-fold K4−e design of order n; i.e., a decomposition of λKn into copies of K4−e.
By using the Paley design of order n=(q+1)/4, q≡3 (mod 4) a prime power, a lower bound for the number of Hadamard designs of order q+1 is also obtained.
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These findings shed light on the design of ordered mesoporous alumina-supported materials with high loading of active metal oxides for many high-temperature reactions.
A bull-design of order n is an ordered pair (X,A), where X is the vertex set of Kn and A is an edge-disjoint decomposition of Kn into copies of bulls.
In this paper, it is shown that a bull-design of order n can be embedded in a bull-design of order m if and only if m≥3n/2+1 or m="n.
The purpose of this note is to determine, for each admissible v, the minimum integer n such that any K3-design of order v can be embedded into a (K3+e -design of order n.
A G-design of order v is an edge disjoint decomposition of Kv into copies of the graph G.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com