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3-Wise Exactly 1-Intersecting Families of Sets

✍ Scribed by Zsolt Katona

Book ID: 106047534
Publisher: Springer Japan
Year: 2005
Tongue: English
Weight: 257 KB
Volume: 21
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s00373-004-0592-x

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✦ Synopsis

Let f(l, t, n) be the maximal size of a family F & 2 ½n such that any l ! 2 sets of F have an exactly t ! 1-element intersection. If l ! 3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine f ðl; t; nÞ ¼ l 2 ðn À 1Þ Ä Å þ 1. Let gðl; t; nÞ be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: gð3; 1; nÞ ¼ n 2=3 ð1 þ oð1ÞÞ.

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