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Conditions nécessaires d’existence des ( k , r , s , ) -plans

G. Heuzé (1972)

Mathématiques et Sciences Humaines

Les ( k , r , s ) -plans (définis ci-dessous) ont été introduits dans [1]. Leur étude englobe celle des plans affines et projectifs finis, des familles de carrés latins deux à deux orthogonaux, de certains plans équilibrés et partiellement équilibrés 2 . La question de leur existence est très mal connue, celle de leur unicité n’a pratiquement pas été abordée. Nous nous proposons de montrer le théorème suivant : pour qu’il existe un ( k , r , s ) -plan il est nécessaire que : k ( k - 1 ) ( r - 1 ) s , r ( k - 1 ) ( r - 1 ) s , k r ( k - 1 ) ( r - 1 ) s ( k + r - s - 1 ) soient entiers.

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Mateva, Zlatka (2008)

Serdica Journal of Computing

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.The author developed computer programs needed for the classification of designs with certain automorphisms by the local approach method. All these programs use canonicity test or/and construction of canonical form of an integer matrix. Their efficiency substantially influences the speed of the whole computation. The present paper deals with the implemented canonicity algorithm. It is based on ideas used by McKay, Meringer,...

Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results

Diane M. Donovan, Mike Grannell, Emine Ş. Yazıcı (2020)

Commentationes Mathematicae Universitatis Carolinae

We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of t mutually orthogonal Latin squares of order n to construct a set of 2 t mutually orthogonal Latin squares of order n t .

Construction methods for gaussoids

Tobias Boege, Thomas Kahle (2020)

Kybernetika

The number of n -gaussoids is shown to be a double exponential function in n . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing 3 -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed 3 -minors.

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