In covering based rough sets, the neighborhood of an element is the intersection of all the covering blocks containing the element. All the neighborhoods form a new covering called a covering of neighborhoods. In the course of studying under what condition a covering of neighborhoods is a partition, the concept of repeat degree is proposed, with the help of which the issue is addressed. This pa...

We study a combinatorial problem formulated in terms of the following group-formation scenario. Given some agents, where each agent has preferences over the set of potential group leaders, the task is to partition the agents into groups and assign a group leader to each of them, so that the group leaders have as high support as possible from the groups they are assigned to lead. We model this s...

By Jason Fulman Department of Mathematics, University of Southern California Los Angeles, CA 90089, USA [email protected] Abstract: Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representa...

Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V1, . . . , Vm) of V (G) such that each Vi induces one of stars K1,1, . . . ,K1,n, and (ii) for every subset S of V (G), G\S has at most n|S| components with the property that each of their blocks is an odd order complete graph.

We give a combinatorial proof of Harer and Zagier’s formula for the disjoint cycle distribution of a long cycle multiplied by an involution with no fixed points, in the symmetric group on a set of even cardinality. The main result of this paper is a direct bijection of a set Bp,k , the enumeration of which is equivalent to the Harer–Zagier formula. The elements of Bp,k are of the form ( , ), wh...

Abstrac:-. New technique of robust pole assignment based on angle criterion of root locus for plant with interval parameters is proposed. The proposed approach allows to assign the dominant pole domains of interval system with guaranteed stability margin and damping ratio. The other pole localization domains assigns to the required regions on the base of D – partition technique. The uncertainti...

We present a partitioning technique of functional models that is used in conjunction with high-level synthesis of digital synchronous circuits. The partitioning goal is to synthesize multi-chip systems from one behavioral description, that satisfy both chip area constraints and an overall latency timing constraint. There are three major advantages of using partitioning techniques at the functio...

This paper presents performance results of a new data partitioning technique: snake partitioning , a data decomposition technique than can be derived at compile-time. Snake partitioning is suitable for multidimensional arrays with restricted aane references. The technique derives the data partitioning of these arrays and an execution order that exploits locality in loops. Experiments that compa...

We define M-sequence non-squashing partitions, which specialize to m-ary partitions Sloane, among others), factorial partitions, and numerous other general partition families of interest. We establish an exact formula, various combinatorial interpretations, as well as the asymptotic growth of M-sequence non-squashing partition functions, functions whose associated generating functions are non-m...