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V tomto článku se zabýváme návazností populární karetní hry dobble na kombinatorické struktury. Ukazujeme, že existence dokonalých balíčků karet souvisí s existencí konečných projektivních rovin a systémů ortogonálních latinských čtverců. Dále pomocí obecnější struktury, blokových schémat, diskutujeme možnosti vytváření balíčků karet pro hry s modifikovanými pravidly. Výklad, příklady i přílohy jsou uzpůsobeny tomu, aby si čtenář mohl relativně jednoduše vytvořit vlastní karetní systémy.
Our aim is to demonstrate how the apparatus of groupoid terms (on two variables) might be employed for studying properties of parallelism in the so called -quasigroups. We show that an incidence structure associated with a medial quasigroup of type , , is either an affine space of dimension at least three, or a desarguesian plane. Conversely, if we start either with an affine space of order and dimension , or with a desarguesian affine plane of order then there is a medial quasigroup of...
The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping there exists a point such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of which were previously known (as far as the author knows) only for f linear (cf. [1]).
One of the most outstanding problems in combinatorial mathematics
and geometry is the problem of existence of finite projective planes
whose order is not a prime power.
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