Finite distributive lattices, polyominoes and ideals of K\"onig type

TL;DR

This paper classifies finite distributive lattices and certain polyominoes based on the property that their associated ideals are of K"onig type, linking lattice theory, combinatorics, and algebra.

Contribution

It provides a classification of finite distributive lattices and polyominoes with ideals of K"onig type, expanding understanding of their algebraic and combinatorial properties.

Findings

Classification of finite distributive lattices with K"onig type ideals

Identification of polyominoes with K"onig type ideals

Connection between lattice theory, polyominoes, and algebraic ideals

Abstract

Finite distributive lattices whose join-meet ideals are of K\"onig type will be classified. Furthermore, a class of polyominoes whose polyomino ideals are of K\"onig type will be studied.