The Monoids of Orders Eight, Nine & Ten

A Distler; Thomas William Kelsey

doi:10.1007/s10472-009-9140-y

The Monoids of Orders Eight, Nine & Ten

Research output: Contribution to journal › Article › peer-review

Abstract

We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and anti-isomorphism, there are 858,977 monoids of order eight; 1,844,075,697 monoids of order nine and 52,991,253,973,742 monoids of order ten.

Original language	English
Pages (from-to)	3-21
Number of pages	19
Journal	Annals of Mathematics and Artificial Intelligence
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/s10472-009-9140-y
Publication status	Published - May 2009

Keywords

Monoids
Enumeration combinatorics
AI search

Access to Document

10.1007/s10472-009-9140-y

Cite this

@article{e0242851de4c4abead8f8da985b4fe27,

title = "The Monoids of Orders Eight, Nine & Ten",

abstract = "We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and anti-isomorphism, there are 858,977 monoids of order eight; 1,844,075,697 monoids of order nine and 52,991,253,973,742 monoids of order ten.",

keywords = "Monoids, Enumeration combinatorics, AI search",

author = "A Distler and Kelsey, {Thomas William}",

year = "2009",

month = may,

doi = "10.1007/s10472-009-9140-y",

language = "English",

volume = "56",

pages = "3--21",

journal = "Annals of Mathematics and Artificial Intelligence",

issn = "1012-2443",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - The Monoids of Orders Eight, Nine & Ten

AU - Distler, A

AU - Kelsey, Thomas William

PY - 2009/5

Y1 - 2009/5

N2 - We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and anti-isomorphism, there are 858,977 monoids of order eight; 1,844,075,697 monoids of order nine and 52,991,253,973,742 monoids of order ten.

AB - We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order ten or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and anti-isomorphism, there are 858,977 monoids of order eight; 1,844,075,697 monoids of order nine and 52,991,253,973,742 monoids of order ten.

KW - Monoids

KW - Enumeration combinatorics

KW - AI search

UR - http://www.scopus.com/inward/record.url?scp=70350722107&partnerID=8YFLogxK

UR - http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s10472-009-9140-y

U2 - 10.1007/s10472-009-9140-y

DO - 10.1007/s10472-009-9140-y

M3 - Article

SN - 1012-2443

VL - 56

SP - 3

EP - 21

JO - Annals of Mathematics and Artificial Intelligence

JF - Annals of Mathematics and Artificial Intelligence

IS - 1

ER -

The Monoids of Orders Eight, Nine & Ten

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

The semigroups of order 10

Cite this

The Monoids of Orders Eight, Nine & Ten

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Research output

The semigroups of order 10

Cite this