Some Properties of Inclusions of Multisets and Contractive Boolean Operators
Combinatorics
2014-04-02 v6
Abstract
Consider the following curious puzzle: call an n-tuple X=(X_1, ..., X_n) of sets smaller than another n-tuple Y if it has fewer //unordered sections//. We show that equivalence classes for this preorder are very easy to describe and characterize the preorder in terms of the simpler pointwise inclusion and the existence of a special increasing boolean operator f:B^n -> B^n. We also show that contrary to increasing boolean operators, the relevant operators are not finitely generated, which might explain why this preorder is not easy to describe concretely.
Keywords
Cite
@article{arxiv.1106.3874,
title = {Some Properties of Inclusions of Multisets and Contractive Boolean Operators},
author = {Pierre Hyvernat},
journal= {arXiv preprint arXiv:1106.3874},
year = {2014}
}
Comments
10 pages, including appendix