First, Cogis and Habib (RAIRO Inform. 7Mor. 13 (1979), 3-18) solved the jump number problem for series-parallel partially ordered sets (posets) by applying the greedy algorithm and then Rival (Proc. Amer. Math. Sot. 89 (1983). 387-394) extended their result to N-free posets. The author (Order 1 (1984), 7-19) provided an interpretation of the latter result in the terms of arc diagrams of posets ...

In the lattice of subsets of an n-set X , every maximal Sperner family S may be partitioned into disjoint subfamilies A and B, such that the union of the upset of A with the downset of B yields the entire lattice: U(A) [ D(B) = 2 X . The result generalizes to certain posets.

Effect algebras ([1], [2]) and D-posets ([3]) are equivalent systems important in quantum structures. In the paper an independent sequence of observables is defined by such a way that a very general version of the central limit theorem may be proved.

A poset is (3 + 1)-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the (3 + 1)-free conjecture of Stanley and Stembridge. Recently, Lewis and Zhang have enumerated graded (3+1)-free posets, but until now the general enumeration problem has remained open. We enumerate all (3 + 1)-free posets by giving a decomposit...

In this paper we study shellable posets (partially ordered sets), that is, finite posets such that the simplicial complex of chains is shellable. It is shown that all admissible lattices (including all finite semimodular and supersolvable lattices) and all bounded locally semimodular finite posets are shellable. A technique for labeling the edges of the Hasse diagram of certain lattices, due to...

In 1981, Kelly showed that planar posets can have arbitrarily large dimension. However, the posets in Kelly’s example have bounded Boolean dimension and bounded local dimension, leading naturally to the questions as to whether either Boolean dimension or local dimension is bounded for the class of planar posets. The question for Boolean dimension was first posed by Nešetřil and Pudlák in 1989 a...

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...

In this article we describe a very efficient method to construct pairwise nonisomorphic posets (equivalently, T0 topologies). We also give the results obtained by a computer program based on this algorithm, in particular the numbers of nonisomorphic posets on 15 and 16 points and the numbers of labelled posets and topologies on 17 and 18 points.