Partitions of multisets

✍ Scribed by Edward A. Bender

• Book ID: 103058123
• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 663 KB
• Volume: 9
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(74)90076-4

✦ Synopsis

A multisct is a set with repeated elements. There are four distinct partition numbers tk: consider, unfikc the cla%sica! set partition case which involves only Stirling numbers of thz second kind. Wing inclusion exclusion, we obtain generating functions when each element iq7t)ears txactfy f = I, 2 of 3 times. The cast: t = 1 is classical ;nd f = 2 was studied by Comtet and B~rlStr u&g other methods. Our approach also leads to asymptotic formulae for the total number rrf partitions of n'tuftigts in which the rcpctltion oi' elements is bounded. Another ap prtjach tu multiset enumeration, using de Bruijn's theorem for group reduced distributions, is &x&bed_

I. Introdwtion