a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

We make an attempt to portray the current situation in probabilistic combinatorics field, where so-called generalized allocation scheme has been utilized. give a series of limit theorems for sums independent identically distributed non-negative integer-valued random variables that find their application scheme. say word about phenomenon transition distribution from one lattice another context s...

Transversal Design is a well known combinatorial design that has been used in deterministic key predistribution scheme. Merging of blocks in a design sometimes helps to obtain a key predistribution scheme with better performance. A deterministic merging strategy to merge the blocks has been discussed. Also, a simple key establishment method for transversal design based key predistribution schem...

Combinatorial designs are very effective tools for managing keys in an infrastructure where power and memory are two major constraints. None of the present day wireless technologies takes the advantage of combinatorial designs. In this paper, we have proposed a general framework using combinatorial designs which will enable the participating devices to communicate securely among themselves with...

A combinatorial random variable is a discrete random variable defined over a combinatorial set (e.g., a power set of a given set). In this paper we introduce combinatorial Markov random fields (Comrafs), which are Markov random fields where some of the nodes are combinatorial random variables. We argue that Comrafs are powerful models for unsupervised learning by showing their relationship with...

Sink location is considered as a basic service in geographic routing in wireless sensor networks. Obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. In this paper, a sink location algorithm based on Fano plane is proposed. The research challenge is how to ensure the intersection of two SLQ (Location Q...

Combinatorial designs are very effective tools for managing keys in an infrastructure where power and memory are two major constraints. None of the present day wireless technologies takes the advantage of combinatorial designs. In this paper, we have proposed a general framework using combinatorial designs which will enable the participating devices to communicate securely among themselves with...

This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group G is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated.

We study the Mathias-Prikry and Laver-Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martin’s number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias-Prikry forcing does not add any dominating reals.