Given a set U n þinspace=þinspace\0,1,...,nþinspace−þinspace1\, a collection \$\backslashmathcal\M\\$ of subsets of U n that is closed under intersection and contains U n is known as a Moore family. The set of Moore families for a given n, denoted by M n , increases very quickly with n, thus |M 3| is 61 and |M 4| is 2480. In 1 the authors determined the number for nþinspace=þinspace6 and stated a 24h- computation-time. Thus, the number for nþinspace=þinspace7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for nþinspace=þinspace7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.
%0 Book Section
%1 Colomb2010
%A Colomb, Pierre
%A Irlande, Alexis
%A Raynaud, Olivier
%B Formal Concept Analysis: 8th International Conference, ICFCA 2010, Agadir, Morocco, March 15-18, 2010. Proceedings
%C Berlin, Heidelberg
%D 2010
%E Kwuida, Léonard
%E Sertkaya, Barıs
%I Springer Berlin Heidelberg
%K combinatorics fca moore_families number
%P 72--87
%R 10.1007/978-3-642-11928-6_6
%T Counting of Moore Families for n=7
%U https://doi.org/10.1007/978-3-642-11928-6_6
%X Given a set U n þinspace=þinspace\0,1,...,nþinspace−þinspace1\, a collection \$\backslashmathcal\M\\$ of subsets of U n that is closed under intersection and contains U n is known as a Moore family. The set of Moore families for a given n, denoted by M n , increases very quickly with n, thus |M 3| is 61 and |M 4| is 2480. In 1 the authors determined the number for nþinspace=þinspace6 and stated a 24h- computation-time. Thus, the number for nþinspace=þinspace7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for nþinspace=þinspace7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.
%@ 978-3-642-11928-6
@inbook{Colomb2010,
abstract = {Given a set U n {\thinspace}={\thinspace}{\{}0,1,...,n{\thinspace}−{\thinspace}1{\}}, a collection {\$}{\backslash}mathcal{\{}M{\}}{\$} of subsets of U n that is closed under intersection and contains U n is known as a Moore family. The set of Moore families for a given n, denoted by M n , increases very quickly with n, thus |M 3| is 61 and |M 4| is 2480. In [1] the authors determined the number for n{\thinspace}={\thinspace}6 and stated a 24h- computation-time. Thus, the number for n{\thinspace}={\thinspace}7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for n{\thinspace}={\thinspace}7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.},
added-at = {2017-12-21T19:28:57.000+0100},
address = {Berlin, Heidelberg},
author = {Colomb, Pierre and Irlande, Alexis and Raynaud, Olivier},
biburl = {https://www.bibsonomy.org/bibtex/2d47b2eb73343126a153e8039720dd50c/tomhanika},
booktitle = {Formal Concept Analysis: 8th International Conference, ICFCA 2010, Agadir, Morocco, March 15-18, 2010. Proceedings},
doi = {10.1007/978-3-642-11928-6_6},
editor = {Kwuida, L{\'e}onard and Sertkaya, Bar{\i}{\c{s}}},
interhash = {54f0c4f4c1aa451dd564e38cd33da56f},
intrahash = {d47b2eb73343126a153e8039720dd50c},
isbn = {978-3-642-11928-6},
keywords = {combinatorics fca moore_families number},
pages = {72--87},
publisher = {Springer Berlin Heidelberg},
timestamp = {2017-12-21T19:28:57.000+0100},
title = {Counting of Moore Families for n=7},
url = {https://doi.org/10.1007/978-3-642-11928-6_6},
year = 2010
}