Семинар за примењену математику, 22. јун 2010.

• 21. Јун, 2010
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Детаљније:

Наредни састанак Семинара за примењену математику одржаће се у уторак, 22.06.2010. у 14:15 у сали 301ф МИ САНУ.

Предавач: Александар Јуришић, Faculty of Computer and Information Science, University of Ljubljana

Назив предавања: USE OF ORTHOGONAL POLYNOMIALS IN DISCRETE MATHEMATICS

Abstract:

Orthogonal polynomials were developed in the late 19th century from a study of continued fractions by Chebyshev and were pursued by Markov, Stieltjes and by a few other mathematicians. Since then, applications have been developed in many areas of mathematics and physics. In our talk we will concentrate on their applications in discrete mathematics. For example, we show how to use them to improve efficient implementations of cryptosystems based on finite fields and in particular on elliptic curves. Most finite objects of sufficient regularity are closely related to certain distance-regular graphs, which can be in turn treated as combinatorial interpretations of certain orthogonal polynomials. We will exploit these connections and finally, we show that the determinant of a Toplitz matrix can be written as a product of two determinants of approximately half the size of the original one.

Предавач: Матјаж Урлеп, PhD student, Faculty of Computer and Information Science, University of Ljubljana

Назив предавања: NONEXISTANCE OF CERTAIN DISTANCE-REGULAR GRAPHS

Abstract:

We prove that a distance-regular graph with the intersection array $$ \{(2r+1)(2r^2-1), 4r(r^2-1), 2r^2; 1, 2(r^2-1), 2r(2r^2-1)\}$$ for $r>1$ does not exist. First, the nonexistence is proven for $r>3$ by using triple intersection numbers and an equality in Krein conditions. Later, a more general proof for $r > 1$ is given, which also makes use of the balanced set condition due to Terwilliger.