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Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

Given a groupoid 〈 G , ☆ 〉 , and k ≥ 3 , we say that G is antiassociative if an only if for all x 1 , x 2 , x 3 ∈ G , ( x 1 ☆ x 2 ) ☆ x 3 and x 1 ☆ ( x 2 ☆ x 3 ) are never equal. Generalizing this, 〈 G , ☆ 〉 is k -antiassociative if and only if for all x 1 , x 2 , ... , x k ∈ G , any two distinct expressions made by putting parentheses in x 1 ☆ x 2 ☆ x 3 ☆ ⋯ ☆ x k are never equal. We prove that for every k ≥ 3 , there exist finite groupoids that are k -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

Antiflexible Latin directed triple systems

Andrew R. Kozlik (2015)

Commentationes Mathematicae Universitatis Carolinae

It is well known that given a Steiner triple system one can define a quasigroup operation · upon its base set by assigning x · x = x for all x and x · y = z , where z is the third point in the block containing the pair { x , y } . The same can be done for Mendelsohn triple systems, where ( x , y ) is considered to be ordered. But this is not necessarily the case for directed triple systems. However there do exist directed triple systems, which induce a quasigroup under this operation and these are called Latin directed triple systems....

Anti-Inverse Semigroups

Stojan Bogdanović, Svetozar Milić, Velimir Pavlović (1978)

Publications de l'Institut Mathématique

Applications de Gauss et pléthysme

Laurent Manivel (1997)

Annales de l'institut Fourier

Les représentations irréductibles de Gl ( n , ℂ ) sont décrites par les foncteurs de Schur, dont la composition définit le pléthysme. Sa compréhension est un problème important en théorie des invariants, ou bien en relation avec les représentations des groupes symétriques.Nous proposons dans cet article une approche géométrique du problème. Généralisant les plongements classiques de Veronese et de Segre, nous construisons des plongements de variétés de drapeaux dans d’autres variétés de drapeaux, sur lesquels...

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