Polynomial functions over bounded distributive lattices

TL;DR

This paper characterizes polynomial functions over bounded distributive lattices, providing multiple descriptions and exploring their disjunctive normal form representations, thus advancing the understanding of lattice polynomial functions.

Contribution

It offers new characterizations and normal form representations for polynomial functions on bounded distributive lattices, extending existing theoretical frameworks.

Findings

Multiple characterizations of polynomial functions

Disjunctive normal form representations derived

Enhanced understanding of lattice polynomial functions

Abstract

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and meets. Moreover, we discuss the disjunctive normal form representations of these polynomial functions.