Building everything from scratch, we give another proof of Propp and Roby’s theorem saying that the average antichain size in any reverse operator orbit of the poset [m] × [n] is mn m+n . It is conceivable that our method should work for other situations. As a demonstration, we show that the average size of antichains in any reverse operator orbit of [m] ×Kn−1 equals 2mn m+2n−1 . Here Kn−1 is t...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

Poset games are two-player impartial combinatorial games, with normal play convention. Starting with any poset, the players take turns picking an element of the poset, and removing that and all larger elements from the poset. Examples of poset games include Chomp, Nim, Hackendot, Subset-Takeaway, and others. We prove a general theorem about poset games, which we call the Poset Game Perioidicity...

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbo...

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right con...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...