Abstract: Continued fractions allow to describe naturally the generating function of labelled lattice paths with bounded height. Several combinatorial problems have a natural bijection to these paths and their generating functions are expressible by continued fractions. The denominators of the finite continued fractions are related to families of orthogonal polynomials. The properties of the roots of orthogonal polynomial sequences allow to find explicitly the asymptotic behaviour of some generating functions, as well as parameters related to them. The number of "up" steps in a wide variety of weighted lattice paths of bounded height is shown to be asymptotically normal with linear mean and variance.
Zoom-Meeting beitreten: zoom.us/j/95266898496
Meeting-ID: 952 6689 8496
Kenncode: p291Sc