An FCA Perspective on n-Distributivity

Abstract

Distributive lattices belong to the best studied ordered structures. A. Huhn introduced a generalisation of this lattice property, called n-distributivity. We present two new methods to recognise the parameter n of this property for a given structure. For this purpose we use the arrow relations in a formal context and implications with proper premise. Additionally, we consider subsets of an order relation ≤ on a finite set P with an additional property. These subsets will be called left clearings of ≤. We show that the family of left clearings forms a complete dually l-distributive lattice, where l denotes the length of (P, ≤ ). Using these results, we determine that parameter n for Tamari lattices for the n-distributivity and dually n-distributivity.