Proof of Ira Gessel's lattice path conjecture
By Manuel Kauers, C. Koutschan, Doron Zeilberger. Proceedings of the National Academy of Sciences of the United States of America, 2008
67 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/9bbec79a1f7c6a75133c5d84beaaeaedffc92d00
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Walks with small steps in the quarter plane (2008, result): “[46] M. Petkovšek, H. S. Wilf, and D. Zeilberger.”
- On 3-Dimensional Lattice Walks Confined to the Positive Octant (2014, unknown): “on,whichdoesnotdetermineQ(x;y;t) uniquely. Threeofthesefourmodelscanbesolvedusingahalf-orbitsum,followed byamoredelicateextractionprocedure[11]. Thefourthonewasfirstsolvedusing intensivecomputeralgebra[23,6],andmorerecentlyusingcomplexanalysis[7]. FormodelsinZ3,italsohappensthatwefindafinitegroupbutano”
- Counting walks in a quadrant: a unified approach via boundary value problems (2010, unknown): “, [5, 12, 13], [4, 16, 17] and [8, 23], respectively).”