Alin Bostan, Manuel Kauers,
"The Complete Generating Function for Gessel Walks is Algebraic"
, in Proceedings of the American Mathematical Society, Vol. 138, Nummer 9, Seite(n) 3063-3078, 9-2010, ISSN: 0002-9939
Original Titel:
The Complete Generating Function for Gessel Walks is Algebraic
Sprache des Titels:
Englisch
Original Kurzfassung:
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.
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