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Binary caps with many free pairs of points
Author(s) -
Lisoněk Petr
Publication year - 2006
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.20117
Subject(s) - combinatorics , mathematics , cardinality (data modeling) , maximization , point (geometry) , binary number , upper and lower bounds , space (punctuation) , discrete mathematics , arithmetic , computer science , geometry , mathematical optimization , mathematical analysis , operating system , data mining
We introduce the following new viewpoint in the study of caps in PG( m , q ). The objective is to maximize, among all caps of given cardinality in a given projective space, the number of free pairs of points, which we define as pairs of points not participating in any coplanar quadruple of points of the cap. We survey the known results (which were motivated by an application in statistical experiment design) and then we improve the known lower bound on the number of free pairs of points for q = 2 and the smallest cap sizes for which the maximization problem is non‐trivial. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 490–499, 2006