ncku-talk2011-05-17

NCTS(South)/ NCKU Math Colloquium

DATE 2011-05-17　14:10-15:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Catherine Yan （Texas A&M University）

TITLE Goncarov Polynomials and Applications in Combinatorics

ABSTRACT We will outline the theory of biorthogonal polynomials, and use this to study combinatorial problems. In particular, we describe the algebraic properties of the sequence of Goncarov polynomials and its various generalizations, which give a unified algebraic approach to several combinatorial objects, including
(1) The cumulative distribution functions of the random vectors of order statistics of $n$ independent random variables with uniform distribution on an interval;
(2) General parking functions, that is, sequences $(x_1, x_2, \dots,x_n)$ of integers whose order statistics are bounded between two given non-decreasing sequences;
(3) Lattice paths that avoid certain general boundaries; and
(4) The area-enumerator of lattice paths avoiding certain general boundaries.

NCTS(South)/ NCKU Math Colloquium

DATE	2011-05-17　14:10-15:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Catherine Yan （Texas A&M University）

TITLE	Goncarov Polynomials and Applications in Combinatorics

ABSTRACT	We will outline the theory of biorthogonal polynomials, and use this to study combinatorial problems. In particular, we describe the algebraic properties of the sequence of Goncarov polynomials and its various generalizations, which give a unified algebraic approach to several combinatorial objects, including (1) The cumulative distribution functions of the random vectors of order statistics of $n$ independent random variables with uniform distribution on an interval; (2) General parking functions, that is, sequences $(x_1, x_2, \dots,x_n)$ of integers whose order statistics are bounded between two given non-decreasing sequences; (3) Lattice paths that avoid certain general boundaries; and (4) The area-enumerator of lattice paths avoiding certain general boundaries.