This talk is scheduled to be given at Fourth International Conference on Combinatorial Mathematics and Combinatorial Computing
Title: Guesseling
Abstract: How does one prove an intriguing and beautiful explicit formula, guessed by Ira Gessel, that a certain set of lattice paths is given by a certain beautiful formula?
"One" GUESSES a much uglier "formula" for a much more general set of lattice paths, then "one" proves it by induction, and then, for the original special case guessed by Ira Gessel, "one" gets an ugly duckling of a "formula" for the original Gessel guess, and finally "one" proves that the ugly "formula" for the special case, is equivalent to the original beautiful swan of Ira Gessel.
Sounds ugly? Well, maybe, but "one" does not mind, since "one" is a computer. But teaching "one" how to perfrom all the steps all by itself, is beautiful, if I do say so myself.
[Joint work with Manuel Kauers, Christoph Kauers, and a "one"].