In this paper, given a poset $(X,leq)$, we introduce some  drifts on a groupoid $(X,*)$ with respect to $(X,leq)$, and we obtain several properties of these drifts related to the notion of $Bin(X)$. We discuss some connections between fuzzy subalgebras and upward drifts.

A partial order or poset   , P X   on a (finite) base set X determines the set   P  of linear extensions of P . The problem of computing, for a poset P , the cardinality of   P  is #P-complete. A set   1 2 , , , k P P P  of posets on X covers the set of linear orders that is the union of the   i P  . Given linear orders 1 2 , , , m L L L  on X , the Poset Cover problem is to de...

We will prove that the path minimizes the number of closed walks of length l among the connected graphs for all l. Indeed, we will prove that the number of closed walks of length l and many other properties such as the spectral radius, Estada index increase or decrease along a certain poset of trees. This poset is a leveled poset with path as the smallest element and star as the greatest element.

We prove that every height-2 finite poset with three or more points has an incomparable pair (.x, J) such that the proportion of all linear extensions of the poset in which s is less than y is between l/3 and 213. A related result of Koml6s says that the containment interval [l/3,2/3] shrinks to [l/2, l/2] in the limit as the width of height-2 posets becomes large. We conjecture that a poset de...

Let Q(k; l) be a poset whose Hasse diagram is a regular spider with k +1 legs having the same length l (cf. Fig. 1). We show that for any n 1 the n th cartesian power of the spider poset Q(k; l) is a Macaulay poset for any k 0 and l 1. In combination with our recent results 2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices, whos...

Let C(L) denote the set of covers of a poset L: γ ∈ C(L) if and only γ = (γ0, γ1) ∈ L×L and the interval {x | γ0 ≤ x ≤ γ1 } is a two elements poset. If L is a lattice then there is a natural ordering of C(L): γ ≤ δ if and only if γ0 ≤ δ0, γ1 6≤ δ0, and γ1 ≤ δ1. That is, γ ≤ δ if and only if the cover γ transposes up to δ. For α ∈ C(L) let C(L,α) denote the component of the poset C(L) connected ...

In this paper we introduce the notion of the total linear discrepancy of a poset as a way of measuring the fairness of linear extensions. If L is a linear extension of a poset P , and x, y is an incomparable pair in P , the height difference between x and y in L is |L(x) − L(y)|. The total linear discrepancy of P in L is the sum over all incomparable pairs of these height differences. The total...

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. ...

We study observables as r-D-homomorphisms de®ned on Boolean D-posets of subsets into a Boolean Dposet. We show that given an atomic r-complete Boolean D-poset P with the countable set of atoms there exist a r-complete Boolean D-poset of subsets S and a r-D-homomorphism h from S onto P, more precisely we can choose S ˆ B…R†, which gives an analogy of the Loomis± Sikorski representation theorem f...

Whereas the Dedekind-MacNeille completion D(P ) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P )∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is joinirreducible). In this paper we study lattices which a...