Some Properties of Inclusions of Multisets and Strictly Increasing Boolean Functions

Details Some Properties of Inclusions of Multisets and Strictly Increasing Boolean Functions Some Properties of Inclusions of Multisets and Strictly Increasing Boolean Functions

2011-06-20

arxiv.org/abs/1106.3874v2

Mathematics

Combinatorics

11 pages, including appendix

Scientific paper

Consider the following curious puzzle: call an $n$-tuple $X=(X_1,...,X_n)$ of sets smaller than $Y$ if it has less //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 strictly increasing boolean function $f:B^n -> B^n$. We also show that contrary to plain boolean functions or increasing boolean functions, strictly increasing boolean functions aren't finitely generated, which might explain why this preorder isn't easily described concretely.

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