Some Properties of Inclusions of Multisets and Strictly Increasing Boolean Functions

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

This short paper contains the result of a small investigation into a curious puzzle: call an n-tuple of sets X = (X1 , . . . , Xn ) smaller than Y if it has less unordered sections. We show that equivalence classes up-to this preorder are very easy to describe (read on to get the answer!) and characterize the preorder in terms of the simpler pointwise inclusion. This gives a simple algorithm for comparing n-tuples of sets. An interesting point is that part of this work relies on the notion of strictly increasing boolean function, which doesn't appear in the traditional literature (??). As an extra, we also show that contrary to plain boolean functions, strictly increasing boolean functions aren't finitely generated.

Mots clés: strictly increasing boolean function; order; multiset

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

Pierre Hyvernat. Some Properties of Inclusions of Multisets and Strictly Increasing Boolean Functions. 2011. ⟨hal-00601505v1⟩