Boolean Dimension of a Boolean Lattice

Marcin Briański (1) , Jędrzej Hodor (1) , Hoang La (1, 2) , Piotr Micek (1) , Katzper Michno (1)

1 Faculty of Mathematics and Computer Science of the Jagiellonian University
2 GALaC - Graphes, Algorithmes et Combinatoire - LISN

For every integer $n$ with $n \geq 6$, we prove that the Boolean dimension of a poset consisting of all the subsets of $\{1,\dots,n\}$ equipped with the inclusion relation is strictly less than $n$.

Domaines: Combinatoire [math.CO]

Marcin Briański, Jędrzej Hodor, Hoang La, Piotr Micek, Katzper Michno. Boolean Dimension of a Boolean Lattice. Order, 2024. ⟨hal-04553148⟩