Let   a family of monomorphisms in the category A ‎To study mathematical notions in a category  A‎, ‎such as injectivity‎, ‎tensor products‎, ‎flatness‎, ‎with respect to a class M of its (mono)morphisms‎, ‎one should know some of the categorical properties of the pair (A ‎,M ‎)‎. ‎In this paper we take A to be the‎‎category  Pos-S  of S-partially ordered sets  and   to be a particular‎ class o...

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fixed point theorems.

The paper considers a generalization of the standard completion of a partially ordered set through the collection of all its lower sets.

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...

We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multiand shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide several (new) results on a class of POPs built on an arbitrary flat poset, obtaining, as corollaries, the bivariate generating function for the distribution of pe...

We generalize the classical notion of majorization in Rn to a majorization order for functions defined on a partially ordered set P . In this generalization we use inequalities for partial sums associated with ideals in P . Basic properties are established, including connections to classical majorization. Moreover, we investigate transfers (given by doubly stochastic matrices), complexity issue...

We introduce the problem of compressing partially ordered strings: given string σ ∈ Σ* and a binary independence relation I over Σ how can we compactly represent an input if the decompressor is allowed to reconstruct any string that can be obtained from σ by repeatedly swapping adjacent independent symbols? Such partially ordered strings are also known as Mazurkiewicz traces, and naturally mode...