2004
DOI: 10.1016/j.jcta.2004.06.007
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Large sets of disjoint packings on 6k+5 points

Abstract: A ð2; 3Þ-packing on X is a pair ðX ; AÞ; where A is a set of 3-subsets (called blocks) of X ; such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph ðX ; EÞ such that E consists of all the pairs which do not appear in any block of A: For a ð6k þ 5Þ-set X a large set of maximum packing, denoted by LMPð6k þ 5Þ; is a set of 6k þ 1 disjoint ð2; 3Þ-packings on X with a cycle of length four as their common leave. Schellenberg and Stinson (J. Combin. Math. Combin. Comp… Show more

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Cited by 27 publications
(60 citation statements)
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“…Denote its block set by D A . So D A can be partitioned into g(m|A| + r − 2) disjoint block sets , j) is the block set of a GDD(2, 3, gm|A| + gr) of type g m(|A|−1) (gm + gr) 1 with the long group G x ∪ S 1 , and such that each…”
Section: Theorem 42 Suppose That There Exists An E-fg(3mentioning
confidence: 99%
“…Denote its block set by D A . So D A can be partitioned into g(m|A| + r − 2) disjoint block sets , j) is the block set of a GDD(2, 3, gm|A| + gr) of type g m(|A|−1) (gm + gr) 1 with the long group G x ∪ S 1 , and such that each…”
Section: Theorem 42 Suppose That There Exists An E-fg(3mentioning
confidence: 99%
“…In [2], the partitionable candelabra system was introduced. It was also used to give a new existence proof of large sets of disjoint triple system [10].…”
Section: A Construction For Lktss Via 2-resolvable Sqssmentioning
confidence: 99%
“…When K = {k}, we simply write k for K . A candelabra system with t = 3 and K = {4} is called a candelabra quadruple system and denoted by C QS(g n 1 1 g n 2 2 · · · g n r r : s). A candelabra system of type (1 v : 0) is usually called a t-wise balanced design and denoted by S(t, K , v).…”
Section: A Construction For Large Sets Of Q(v)l-intersecting Sts(v)mentioning
confidence: 99%