Partitions with certain intersection properties

✍ Scribed by Péter M. Gergely

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 107 KB
• Volume: 19
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20290

✦ Synopsis

Partitions of the n-element set are considered. A family of m such partitions is called an (n,m,k)-pamily, if there are two classes for any pair of partitions whose intersection has at least k elements, and any pair of elements is in the same class for at most two partitions. Let f(n,k) denote the maximum of m for which an (n,m,k)-pamily exist. A constructive lower bound is given for f(n,k), which is compared with the trivial upper bound. q 2011 Wiley