Definition, Betydelse & Anagram | Engelska ordet POSETS

Definition av POSETS

1. böjningsform av poset

Exempel på hur man kan använda POSETS i en mening

• A Galois connection can also be defined on preordered sets or classes; this article presents the common case of posets.
• That article also discusses how we may rephrase the above definition in terms of the existence of suitable Galois connections between related posets — an approach of special interest for category theoretic investigations of the concept.
• Their theory is a vast generalisation of upper sets in posets, and Yoneda's representability theorem generalizes Cayley's theorem in group theory.
• We can recover the poset S from the nerve NS and the category C from the nerve NC; in this sense simplicial sets generalize posets and categories.
• The cofinal relation over partially ordered sets ("posets") is reflexive: every poset is cofinal in itself.
• The wrinkle is that (for interesting posets) it can be proved that there simply is no such generic subset of the poset.
• Further achievements include proving with Stanisław Radziszowski that the Ramsey number R(4,5) = 25; proving with Radziszowski that no 4-(12, 6, 6) combinatorial designs exist, determining with Gunnar Brinkmann, the number of posets on 16 points, and determining with Ian Wanless the number of Latin squares of size 11.
• Stanley introduced a generalization of the h-vector, the toric h-vector, which is defined for an arbitrary ranked poset, and proved that for the class of Eulerian posets, the Dehn–Sommerville equations continue to hold.
• If A, B are posets, a function f: A → B is residuated if and only if the preimage under f of every principal down-set of B is a principal down-set of A.

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