Research Article

Associative Binary Operations on a Set with Five Elements

by  Amit Sehgal, Ravinder Kumar, Ombir Dahiya
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 76 - Issue 6
Published: August 2013
Authors: Amit Sehgal, Ravinder Kumar, Ombir Dahiya
10.5120/13252-0725
PDF

Amit Sehgal, Ravinder Kumar, Ombir Dahiya . Associative Binary Operations on a Set with Five Elements. International Journal of Computer Applications. 76, 6 (August 2013), 27-33. DOI=10.5120/13252-0725

                        @article{ 10.5120/13252-0725,
                        author  = { Amit Sehgal,Ravinder Kumar,Ombir Dahiya },
                        title   = { Associative Binary Operations on a Set with Five Elements },
                        journal = { International Journal of Computer Applications },
                        year    = { 2013 },
                        volume  = { 76 },
                        number  = { 6 },
                        pages   = { 27-33 },
                        doi     = { 10.5120/13252-0725 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2013
                        %A Amit Sehgal
                        %A Ravinder Kumar
                        %A Ombir Dahiya
                        %T Associative Binary Operations on a Set with Five Elements%T 
                        %J International Journal of Computer Applications
                        %V 76
                        %N 6
                        %P 27-33
                        %R 10.5120/13252-0725
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

Associativity of a binary operation is one of most fundamental property in algebra. The number of binary operation on a set of only five elements is as large as 298,023,223,876,953,125. In this paper, the authors give the answer of the question "How many binary operations on a five elements are associative?" The main goal of this paper is to extend [3] and [5] for five element set.

References
  • Man-Keung Siu, Which Latin Squares are Cayley Tables?, AMS Monthly , 98 (1991) 625-627
  • Fri?rik Diego and Krist?n Halla J?nsd?tti? , Associative Operations on a Three-Element Set, TMME, vol 5, nos2 &3 , pp 257-268, 2008
  • Amit Sehgal and ManMohan , Associative Binary operation on a set with Three elements, International Journal of Essential Sciences, Vol 5, No. 1, pp1-8,2011 (ISSN:0973-8436)
  • Sarita and Amit Sehgal, Using Partition Calculation for number of associative operation is reduced. Proceeding of International Conference on Mathematics and Soft Computing (Application in Engineering) pp437-446 Dec 4-5,2010
  • Amit Sehgal, Sarita and Sunil Dua, Associative Binary operation on a set with Four elements, International Journal of Computer Science and Communication Engineering Volume 1 Issue 2 paper id IJCSCE 121204, 2013 (ISSN:2319-7080)
  • George E. Forsythe, Swac Computers 126 distinct semi groups of order 4 Proc. Amer. Math. Soc. 6 (1955), 443-447.
  • Lyle Ramshaw, The On-Line Encyclopedia of Integer Sequences -A023814 (Number of associative binary operations on an n-set
  • A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv: 1301. 6023, 2013.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

binary operations associativity isomorphism order Partition

Powered by PhDFocusTM