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Statisch pairs in atomistic posets

Alireza Vaezi, Vilas Kharat (2017)

Mathematica Bohemica

We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. ∇ -relation...

Supremum properties of Galois-type connections

Árpád Száz (2006)

Commentationes Mathematicae Universitatis Carolinae

In a former paper, motivated by a recent theory of relators (families of relations), we have investigated increasingly regular and normal functions of one preordered set into another instead of Galois connections and residuated mappings of partially ordered sets. A function f of one preordered set X into another Y has been called (1) increasingly   g -normal, for some function g of Y into X , if for any x ∈ X and y ∈ Y we have f ( x ) ≤ y if and only if x ≤ g ( y ) ; (2) increasingly ϕ -regular, for some function ϕ of X into itself,...

Sur le nombre d'éléments des niveaux des produits de chaînes et des treillis permutoèdres

Bruno Leclerc (1990)

Mathématiques et Sciences Humaines

Les produits de chaînes comptent parmi les ensembles (partiellement) ordonnés les plus fréquemment rencontrés. On rappelle, avec des démonstrations en partie nouvelles, divers résultats exacts ou approchés sur les cardinaux de leurs niveaux et sur le nombre de ses niveaux de cardinal maximum. Un plongement avec de bonnes propriétés permet d'appliquer ces résultats aux niveaux du permutoèdre (ordre faible de Bruhat sur les permutations).

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