Counting sub-multisets of fixed cardinality
Combinatorics
2015-11-20 v1
Abstract
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by sampling without replacement from a finite population partitioned into subsets, in the case where items belonging to the same subset are considered indistinguishable. Despite the generality of this problem, we have been unable to find this result published elsewhere.
Cite
@article{arxiv.1511.06142,
title = {Counting sub-multisets of fixed cardinality},
author = {Sebastiano Ferraris and Alex Mendelson and Gerardo Ballesio and Tom Vercauteren},
journal= {arXiv preprint arXiv:1511.06142},
year = {2015}
}
Comments
9 pages