It is NP-complete to determine whether a given ordered set has a fixed point free orderpreserving self-map. On the way to this result, we establish the NP-completeness of a related problem: Given ordered sets P and Q with t-tuples (PI,. ,pt) and (41,. . , qt) from P and Q respectively, is there an order-preserving map f: P + Q satisfying f(pz) > qr for each i = l,...,t? Mathematics Subject Clas...

In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for certain special cases, and a recursive technique to exactly enumerate the appropriate set partitions in general. We also give some asymptotic results for the growth rates of the number of ordered set partitions avoiding a single pattern; includ...

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the...

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The latticeK(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closu...

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map fr...

1 Department of Computer Science. University of Seville. Spain. {aguilar, riquelme, mtoro}@lsi.us.es Abstract. In this paper, an editing algorithm based on the projection of the examples in each dimension is presented. The algorithm, that we have called EOP (Editing by Ordered Projection) has some interesting characteristics: important reduction of the number of examples from the database; lowe...

The set of isotopy classes ordered n-component links in the 3-sphere is acted on by symmetric group via permutation components. intrinsic symmetry link, S(L), defined to be elements that preserve type L as an unoriented link. study these groups was initiated 1969, but question whether or not every subgroup arises intrinisic some link has remained open. We provide counterexamples; particular, if...