The semigroups of order 10

Andreas Distler, Christopher Anthony Jefferson, Tom Kelsey, Lars Kotthoff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

Abstract

The number of finite semigroups increases rapidly with the number of elements. Since existing counting formulae do not give the complete number of semigroups of given order up to equivalence, the remainder can only be found by careful search. We describe the use of mathematical results combined with distributed Constraint Satisfaction to show that the number of non-equivalent semigroups of order 10 is 12,418,001,077,381,302,684. This solves a previously open problem in Mathematics, and has directly led to improvements in Constraint Satisfaction technology.
Original languageEnglish
Title of host publicationPrinciples and Practice of Constraint Programming
Subtitle of host publication18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012. Proceedings
EditorsMichela Milano
PublisherSpringer
Pages883-899
Number of pages17
ISBN (Electronic)978-3-642-33558-7
ISBN (Print)978-3-642-33557-0
DOIs
Publication statusPublished - 2012
Event18th International Conference on Principles and Practice of Constraint Programming, CP 2012 - Quebec, Canada
Duration: 8 Oct 201212 Oct 2012

Publication series

NameLecture Notes in Computer Science
Volume7514
ISSN (Print)0302-9743

Conference

Conference18th International Conference on Principles and Practice of Constraint Programming, CP 2012
Country/TerritoryCanada
CityQuebec
Period8/10/1212/10/12

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