Some Properties of Inclusions of Multisets and Contractive Boolean Functions

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

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 boolean function $f:B^n -> B^n$. We also show that contrary to plain boolean functions or increasing boolean functions, the relevant boolean functions are not finitely generated, which might explain why this preorder is not easy to describe concretely.

Mots clés: contractive boolean function; system of representatives; multiset

Domaines: Combinatoire [math.CO]; Mathématiques générales [math.GM]

Pierre Hyvernat. Some Properties of Inclusions of Multisets and Contractive Boolean Functions. 2011. ⟨hal-00601505v5⟩