TY - JOUR
T1 - Proof of Ira Gessel's lattice path conjecture
AU - Kauers, Manuel
AU - Koutschan, Christoph
AU - Zeilberger, Doron
PY - 2009/7/14
Y1 - 2009/7/14
N2 - We present a computer-aided, yet fully rigorous, proof of Ira Gessel's tantalizingly simply stated conjecture that the number of ways of walking 2n 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 16n (5/6)n(1/2)n/(5/3)n(2)n.
AB - We present a computer-aided, yet fully rigorous, proof of Ira Gessel's tantalizingly simply stated conjecture that the number of ways of walking 2n 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 16n (5/6)n(1/2)n/(5/3)n(2)n.
KW - Holonomic ansatz
KW - Quarter plane
KW - Walks
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U2 - 10.1073/pnas.0901678106
DO - 10.1073/pnas.0901678106
M3 - Article
AN - SCOPUS:67650915118
SN - 0027-8424
VL - 106
SP - 11502
EP - 11505
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 28
ER -