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On the classification of linear spaces of order 11
Author(s) -
Pietsch Ch.
Publication year - 1995
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.3180030305
Subject(s) - mathematics , enumeration , combinatorics , order (exchange) , generalization , automorphism , linear space , line (geometry) , space (punctuation) , linear span , set (abstract data type) , discrete mathematics , mathematical analysis , geometry , linguistics , philosophy , finance , computer science , economics , programming language
A linear space of order n is a pair ( V,B ), where V is a finite set of n elements and B is a set of subsets of V such that each 2‐subset of V is contained in exactly one element of B. The exact number of nonisomorphic linear spaces was known up to order 10. Betten and Braun [1] found that there exist at least 232,923 nonisomorphic linear spaces of order 11. We used a generalization of Ivanov's algorithm for the enumeration of block designs in order to construct all 232,929 linear spaces of order 11. The method used will be described and some data concerning line types, line lengths, and orders of automorphism groups is listed. © 1995 John Wiley & Sons, Inc.