The minimum number of blocks in pairwise balanced designs with maximum block size 4: the final cases
نویسندگان
چکیده
The minimum number of blocks having maximum size precisely four that are required to cover, exactly λ times, all pairs of elements from a set of cardinality v is denoted by g λ (v) (or g (4)(v) when λ = 1). All values of g (4) λ (v) are known except for λ = 1 and v = 17 or 18. It is known that 30 ≤ g(4)(17) ≤ 31 and 32 ≤ g(4)(18) ≤ 33. In this paper we show that g(4)(17) 6= 30 and g(4)(18) 6= 32, thus finalising the determination of g λ (v) for all λ and v.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 36 شماره
صفحات -
تاریخ انتشار 2006