This work is motivated by Nathanson’s recent paper on relatively prime sets and a phi function for subsets of {1, 2, 3, . . . , n}. We establish enumeration formulas for the number of relatively prime subsets and the number of relatively prime subsets of cardinality k of {1, 2, 3, . . . , n} under various constraints. Further, we show how this work links up with the study of multicompositions. ...

A random sieve of the set positive integers N is an infinite sequence nested subsets = S0 ⊃ S1 S2 · such that Sk obtained from Sk−1 by removing elements with indices outside Rk and enumerating remaining inthe increasing order. Here R1 , R2 . a independent copies R ⊂ N. We prove general limit theorems for Sn related functionals, as n → ∞.

Fibonacci polynomial sequence is an extension of sequence. Here we define a generalizing the integer which enumerates number subsets set [n] including no two consecutive even integers. The associated with polynomials. Some basic properties are obtained.

A theorem now known as Sperner's Lemma [5] states that a largest collection of subsets of an n-element set such that no subset contains another is obtained by taking the collection of all the subsets with cardinal [n/2\. (We denote by |*J, resp. [*], the largest integer less than or equal to x, resp. the smallest integer greater than or equal to x.) In other words, the density of a largest anti...

A theorem now known as Sperner’s Lemma [5] states that a largest collection of subsets of an n-element set such that no subset contains another is obtained by taking the collection of all the subsets with cardinal bn=2c. (We denote by bxc, resp. dxe, the largest integer less than or equal to x, resp. the smallest integer greater than or equal to x.) In other words, the density of a largest anti...

A static dictionary is a data structure for storing subsets of a finite universe U , so that membership queries can be answered efficiently. We study this problem in a unit cost RAM model with word size Ω(log |U |), and show that for n-element subsets, constant worst case query time can be obtained using B +O(log log |U |) + o(n) bits of storage, where B = dlog2 (|U | n ) e is the minimum numbe...

In this paper, we introduce and study the concepts of $mathcal{I}_2$-convergence, $mathcal{I}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{I}_2$ denotes the ideal of subsets of $mathbb N times mathbb N$. Also, we study some properties and relations of them.

In our daily lives we assist to an exponential growth of mobile and fixed devices that surround us, though many of them having limited resources, and not even providing an interface screen. In this paper, we present remoteU¡, a middleware that allows the interaction of those devices with users, resorting to simple but expressive programming mechanisms, and providing efficient implementation and...

The avoidance of immune surveillance by malignant plasma cells (PCs) in multiple myeloma (MM) is mediated different mechanisms, among which an induction T cell exhaustion and expansion myeloid-derived suppressor (MDSCs) appear to play substantial roles, but it still a lack data on possible MDSC-mediated exhaustion. aim the present work was evaluate relationship between frequencies MM PCs, MDSCs...

Let S ⊆ Z. The generalized factorial function for S, denoted n!S , is introduced in accordance with theory already established by Bhargava ([4]). Along with several known theorems about these functions, a number of other issues will be explored. This Thesis is divided into 4 chapters. Chapter 1 provides the necessary definitions and offers a connection between the generalized factorial function...