Linear partition error control codes in the γ-metric is a natural generalization of error control codes endowed with the Rosenbloom-Tsfasman(RT) metric [4] to block coding and has applications in different area of combinatorial/discrete mathematics, e.g. in the theory of uniform distribution, experimental designs, cryptography etc. In this paper, we formulate the concept of linear partition cod...

We study cooperation structures with the following property: Given any two feasible coalitions with non-empty intersection, its union is a feasible coalition again. These combinatorial structures have a direct relationship with graph communication situations and conference structures à la Myerson. Characterizations of the Myerson value in this context are provided using the concept of basis for...

Graph Theory is said to have originated with Euler (1707–1783) who was asked to resolve an pastime question of the citizens of Königsberg whether it is possible to traverse all the 7 bridges joining two islands and the mainland, without retracing any path. Euler recognized in this problem the essense of Leibnitz’s interest in founding a new kind of mathematics (“analysis situs”) which might be ...

who found for us all the theorems in combinatorial mathematics we discuss in this paper. Without his help, the paper could not have been written. We also wish to acknowledge the work of New York at Stony Brook, in helping to create a climate at Stony Brook in which communication between mathematicians and social scientists has been greatly facilitated. for their roles in stimulating his interes...

Strong concentration results play a fundamental role in probabilistic combinatorics and theoretical computer science. In this paper, we present several new concentration results developed recently by the author and collaborators. To illustrate the power of these new results, we discuss applications in many different areas of mathematics, from combinatorial number theory to the theory of random ...

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus...

Numerov-type ODE Solvers are widely used for the numerical treatment of second order initial value problems. In this work we present a powerful and efficient symbolic code in Mathematica for the derivation of their order conditions and principal truncation error terms. The relative tree theory for such order conditions is presented along with the elements of combinatorial mathematics, partition...

The concern of this paper is a famous combinatorial formula known under the name “exponential formula”. It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential generating function of a whole structure is equal to the exponential of those of connected substructures. Keeping this descriptive statement as a guideline,...

In the first part of this article we review the general theory of Cherednik algebras and non-symmetric Macdonald polynomials, including a formulation and proof of the fundamental duality theorem in its proper general context. In the last section we summarize some of the combinatorial results in this area which we have recently obtained in collaboration with J. Haglund and N. Loehr. Mathematics ...

Ancykutty Joseph, On Incidence Algebras and Directed Graphs, IJMMS, 31:5(2002), 301-305, studied the incidence algebras of directed graphs. We have extended it to undirected graphs also. In this paper, we have also established a relation between incidence algebras and the labelings and index vectors introduced by R.H. Jeurissen in Incidence Matrix and Labelings of a Graph, Journal of Combinator...