Let Bn be the poset generated by the subsets of [n] with the inclusion as relation and let P be a nite poset. We want to embed P into Bn as many times as possible such that the subsets in di erent copies are incomparable. The maximum number of such embeddings is asymptotically determined for all nite posets P as 1 t(P ) ( n bn/2c ) , where t(P ) denotes the minimal size of the convex hull of a ...

Empty p0 p2 . . . pξ pξ+2 . . . Nonempty p1 p3 . . . pξ+1 pξ+3 . . . where pξ, ξ < α, is descending in P and Nonempty wins the game of length α if he can play α times. A poset P is called weakly α-game-closed if Player Nonempty has a winning strategy in the Banach-Mazur game of length α, where Nonempty is allowed to play at limit stages. P is called strongly α-game-closed if Player Nonempty has...

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...

in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

provide the notation and terminology for this paper. 1. POSET RETRACTS One can prove the following propositions: (1) For all binary relations a, b holds a · b = a b. (2) Let X be a set, L be a non empty relational structure, S be a non empty relational substruc-ture of L, f , g be functions from X into the carrier of S, and f , g be functions from X into the carrier of L. If f = f and g = g and...

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

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 notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

following the idea of $l$-fuzzy neighborhood system as introduced byfu-gui shi, and its generalization to $(l,m)$-fuzzy neighborhood system, the relationship between  $(l,m)$-fuzzy topology and $(l,m)$-fuzzy neighborhood system will be further studied. as an application of the obtained results, we will describe the initial structures of $(l,m)$-fuzzy neighborhood subspaces and $(l,m)$-fuzzy top...

Whereas Stanley, Proctor and others studied Sperner properties of the poset L(k; m) we consider shadows of left-compressed sets and derive asymptotic bounds on their sizes. ? 1999 Elsevier Science B.V. All rights reserved.