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Tue, 16 May 2006 13:08:47 +0200Tue, 16 May 2006 13:08:47 +0200Functions preserving 2-series strict orders
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1737
In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.Rainer Lenzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1737Tue, 16 May 2006 13:08:47 +0200Isotone mappings of levelled strict orders
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1736
Strict order relations are defined as strict asymmetric and transitive binary relations. For classes of so-called levelled strict orders it is analyzed, under which conditions the endomorphism monoids of two relations coincide; in particular the case of direct sums of strict antichains is studied. Further, it is shown that these orders differ in their sets of binary order preserving functions.Rainer Lenzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1736Tue, 16 May 2006 13:08:21 +0200