Journal of Integer Sequences, Vol. 7 (2004), Article 04.1.5

Antichains of Multisets

Goran Kilibarda and Vladeta Jovovic
Faculty of Technology and Metallurgy
University of Belgrade
Karnegijeva 4
11001 Belgrade
Serbia and Montenegro

Abstract:

The problem of enumeration of m-antichains of k-bounded multisets on an n-set is considered. A formula for calculating the cardinality of the corresponding family in terms of the graph theory was obtained. A more general case of multiantichains is also considered. As an illustration the corresponding explicit formulas are given for the case when 1 <= m <= 4, k >= 1 and n >= 0.

(Concerned with sequences A016269 A047707 A051112 A051113 A051114 A051115 A051116 A051117 A051118 A084869 A084870 A084871 A084872 A084873 A084874 A084875 A084876 A084877 A084878 A084879 A084880 A084881 A084882 A084883 A085461 A085462 A085463 A085464 A085465 .)

Received October 14 2003; revised version received January 28 2004. Published in Journal of Integer Sequences February 17 2004.