Rational and algebraic combinatorics

Vladimir N. Remeslennikov,
Omsk Branch of Sobolev Institute of Mathematics of SB RAS,
Omsk, Russia

A combinatoric is a subset R of a free monoid. A combinatoric R is rational (algebraic) if the generating function for R is rational (algebraic). In this series of talks we give an asymptotic classification of such combinatorics as well as some interesting applications of these results to other areas of mathematics and computer science. The audience is assumed to have knowledge of the first three years of a classic university course.