We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (I2 ... m). The resulting family of orbits P(n, m) is shown to have cardinality p(n, m) = (l/n) ∑d│m φ(d) (::.'!~) where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits l(n, m) of the set of all msubsets of an n-set acted upon by the cyclic permutation (12 ... ...

If a decision maker prefers x to y to z, would he choose orderd set [x, z] or [y, x]? This article studies extension of preferences over individual alternatives to an ordered set which is prevalent in closed ballot elections with proportional representation and other real life problems where the decision maker is to choose from groups with an associated hierarchy inside. I introduce five ordina...

Let $S= \{e_1,\,e_2‎, ‎\ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$‎. ‎The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the‎ ‎vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$‎, ‎where $d_i=1$ if $e_i\in M$ and $d_i=0$‎ ‎otherwise‎, ‎for each $i\in\{1,\ldots‎ , ‎k\}$‎. ‎We say $S$ is a global forcing set for maximal matchings of $G$‎ ‎if $...

in this paper, a certain new connectedness of l-fuzzy subsets inl-topological spaces is introduced and studied by means of preclosed sets. itpreserves some fundamental properties of connected set in general topology.especially the famous k. fan’s theorem holds.

Let L denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set (La,⊆) is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in (La,⊆) has a finite or infinite family of minimal forbidden subgraphs.

A pair of linear orders L, L′ on an n-element set V is a concordance pair if the Kendall and Spearman correlation measures between L and L′ coincide. A graph is called concordance graph if it has the same number of induced three-vertex one-edged subgraphs as induced three-vertex twoedged subgraphs. It is known (see Fishburn and Monjardet (2000)) that (L, L′) is a concordance pair if and only if...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

Let F:X-*X be a multifunction on a partially ordered set (X, ¿). Suppose for each pair «iá*2 and for each yi<EF(xi) there is a yi&F{y¿) such that yièyiThen sufficient conditions are given such that multifunctions F satisfying the above condition will have a fixed point. These results generalize the Tarski Theorem on complete lattices, and they also generalize some results of S. Abian and A. B. ...

We consider quasi-martingales indexed by a linearly order set. We show that such processes are isomorphic to a given class of (finitely additive) measures. From this result we easily derive the classical theorem of Stricker as well as the decompositions of Riesz, Rao and the supermartingale decomposition of Doob and Meyer.

The paper is devoted to knowledge discovery from data, taking into account prior knowledge about preference semantics in patterns to be discovered. The data concern a set of situations (objects, states, examples) described by a set of attributes (properties, features, characteristics). The attributes are, in general, divided into condition and decision attributes, corresponding to input and out...