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Le semi-groupe libre des carrés magiques

Lionel Cozar (1996)

Journal de théorie des nombres de Bordeaux

Nous étudions une loi de composition sur les carrés magiques, qui a déjà été introduite dans la littérature, qui munit l'ensemble de tous les carrés magiques d'une structure de semi-groupe (monoïde). Nous prouvons ensuite une conjecture de Adler et Li, ce semi-groupe est libre.

Linear preserver of n × 1 Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

Let A = [ a i j ] m × n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero ( 1 , 1 ) -entry. We characterize all linear maps perserving the set of n × 1 Ferrers vectors over the binary Boolean semiring and over the Boolean ring 2 . Also, we have achieved the number of these linear maps in each case.

Linear programming duality and morphisms

Winfried Hochstättler, Jaroslav Nešetřil (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....

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