Proof of Ira Gessel's Lattice Path Conjecture
The material on this webpage accompanies the article Proof of Ira Gessel's Lattice Path Conjecture by Manuel Kauers, Christoph Koutschan and Doron Zeilberger.We provide the following electronic material:
- a Mathematica notebook Gessel.nb which demonstrates our computations,
- a pdf screenshot Gessel.nb.pdf of the notebook (if you don't have Mathematica),
- the Mathematica package OreGroebnerBasis.m which is required for the computation,
- the data file annGessel.m containing the annihilating operators we start with,
- and the computed output recurrence.
Addendum (added after the publication of our article):
- a shorter recurrence of order 12 that is obtained by a longer computation (without early termination of the elimination procedure, took approximately 10 days),
- the recurrence for the case i=0 and j=1,
- the recurrence for the case i=1 and j=0,
- and the recurrence for the case i=2 and j=0.