Proof of Ira Gessel's lattice path conjecture
- 14 July 2009
- journal article
- Published by National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 106 (28) , 11502-11505
Abstract
We present a computer-aided, yet fully rigorous, proof of Ira Gessel's tantalizingly simply stated conjecture that the number of ways of walking 2 n steps in the region x + y ≥ 0, y ≥ 0 of the square lattice with unit steps in the east, west, north, and south directions, that start and end at the origin, equals 16 n ( 5 / 6 ) n ( 1 / 2 ) n ( 5 / 3 ) n ( 2 ) n .Keywords
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