Some Aspects of Hankel Matrices in Coding Theory and Combinatorics

John Rotramel

Friday, March 26, 2004
11:00 am, 845 Patterson Office Tower

Abstract:

Hankel matrices consisting of Catalan numbers have been analyzed by various authors, yielding several interesting results. Relatively simple forms for their determinants have been proven. Using a form of generalized Catalan numbers yields determinant forms useful in enumerating plane partitions and alternating sign matrixes. Ulrich Tamm discusses these topics in his paper. He also shows how the relationship between Hankel matrixes and orthogonal polynomials allows calculation of the coefficients of the three-term recurrence relation using the Berlekamp-Massey algorithm from coding theory.