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  • @article{RISC3945,
    author = {Alin Bostan and Manuel Kauers},
    title = {{The Complete Generating Function for Gessel Walks is Algebraic}},
    language = {english},
    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. },
    journal = {Proceedings of the AMS},
    volume = {138},
    number = {9},
    pages = {3063--3078},
    isbn_issn = {ISSN 0002-9939},
    year = {2010},
    month = {September},
    refereed = {yes},
    length = {16}
    }