Finding the standard model of particle physics a combinatorial problem

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constraints. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang–Mills–Higgs models.Program summaryTitle of program:ko0 and ko6Catalogue identifier:ADZZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:4875No. of bytes in distributed program, including test data, etc.:29 933Distribution format:tar.gzProgramming language used:C++Computer:Simple PCOperating system:Any, where C++ runsRAM:Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, a few KB to some MBClassification:5, 11.1Nature of problem:Automatised classification of almost-commutative geometries via Krajewski diagrams.Solution method:Combinatorial generation of all possible Krajewski diagrams and identification of the irreducible ones. Equivalence classes of irreducibles = classification.Running time:  Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, running time reaches from seconds (3×33×3) to weeks (6×66×6) on a standard PC.