Algebraic Combinatorics Seminar
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UNIVERSITY OF KENTUCKY **

ALGEBRAIC COMBINATORICS SEMINAR

845 PATTERSON OFFICE TOWER

FALL 2005

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

Guoce Xin

University of Kentucky

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Monday, November 14, 2005

3:00 pm, 845 Patterson Office Tower

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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.