"Lattice paths, Hankel determinants and the 14-periodicity theorem"

Guoce Xin
University of Kentucky

Monday, November 14, 2005
3:00 pm, 845 Patterson Office Tower

Abstract:

Let M(n,L) be the number of lattice paths from (0,0) to (n,0) with allowing steps (1,1), (1,-1) and (L,0) and is restricted to be above the horizontal line. Then for L=0,1,2, M(n,L) counts the number of Dyck paths, Motzkin paths, and Schroder paths respectively. The Hankel determinants of these numbers are known to have simple form. We prove that for L=3, the Hankel determinants have a period of 14. The first 14 determinants are 1,1,0,0,-1,-1,-1 followed by the negative of the above.