Abstract
Gessel walks are lattice walks in the quarter plane $\set N^2$ which start at the origin~$(0,0)\in\set N^2$ and consist only of steps chosen from the set $\{\leftarrow,\penalty0\swarrow,\penalty0\nearrow,\penalty0\rightarrow\}$. We prove that if $g(n;i,j)$ denotes the number of Gessel walks of length~$n$ which end at the point~$(i,j)\in\set N^2$, then the trivariate generating series $\displaystyle\smash{ G(t;x,y)=\sum_{n,i,j\geq 0} g(n;i,j)x^i y^j t^n } $ is an algebraic function.
| Original language | English |
|---|---|
| Pages (from-to) | 3063-3078 |
| Number of pages | 16 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 138 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - Sept 2010 |
Fields of science
- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101003 Applied geometry
- 102025 Distributed systems
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)