A computation of the ninth Dedekind number
Christian Jäkel
Abstract
In this article, we present an algorithm to compute the 9th Dedekind number: 286386577668298411128469151667598498812366. The key aspects are the use of matrix multiplication and symmetries in the free distributive lattice, that are determined with techniques from Formal Concept Analysis.
Topics & Concepts
Distributive propertyDedekind sumNinthDistributive latticeDedekind cutComputationMultiplication (music)Lattice (music)MathematicsKey (lock)Homogeneous spaceCongruence lattice problemArithmeticComputer scienceAlgebra over a fieldPure mathematicsAlgorithmCombinatoricsPhysicsAcousticsComputer securityGeometryRough Sets and Fuzzy LogicAdvanced Algebra and LogicLogic, Reasoning, and Knowledge