The Quasi-Holonomic Ansatz and Restricted Lattice Walks
| dc.creator | Kauers, Manuel | |
| dc.creator | Zeilberger, Doron | |
| dc.date | 2008-06-26 | |
| dc.date.accessioned | 2026-07-07T09:46:55Z | |
| dc.date.available | 2026-07-07T09:46:55Z | |
| dc.description | The great enumerator Germain Kreweras empirically discovered this intriguing fact, and then needed lots of pages[K], and lots of human ingenuity, to prove it. Other great enumerators, for example, Heinrich Niederhausen[N], Ira Gessel[G1], and Mireille Bousquet-Mélou[B], found other ingenious, ``simpler'' proofs. Yet none of them is as simple as ours! Our proof (with the generous help of our faithful computers) is ``ugly'' in the traditional sense, since it would be painful for a lowly human to follow all the steps. But according to our humble aesthetic taste, this proof is much more elegant, since it is (conceptually) one-line. So what if that line is rather long (a huge partial-recurrence equation satisfied by the general counting function), it occupies less storage than a very low-resolution photograph. | |
| dc.description | A One-Line Proof of Kreweras' Quarter-Plane Walk Theorem. See: http://www.math.rutgers.edu/~zeilberg/tokhniot/oKreweras | |
| dc.identifier | https://arxiv.org/abs/0806.4318 | |
| dc.identifier | http://arxiv.org/abs/0806.4318 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163697 | |
| dc.subject | Combinatorics | |
| dc.subject | 33F10; 05A10 | |
| dc.title | The Quasi-Holonomic Ansatz and Restricted Lattice Walks | |
| dc.type | text |