@InProceedings{   BousquetMelou:2002,
  Author        = "Bousquet-M{\'e}lou, Mireille",
  Editor        = "Chauvin, Brigitte and Flajolet, Philippe and Gardy, Dani{\`e}le and Mokkadem, Abdelkader",
  Abstract      = "We study planar walks that start from a given point (i0j0), take their steps in a finite set {\$}{\$}{\backslash}mathfrak{\{}S{\}}{\$}{\$}, and are confined in the first quadrant x ≥ 0, y ≥ 0. Their enumeration can be attacked in a systematic way: the generating function Q(x, y; t) that counts them by their length (variable t) and the coordinates of their endpoint (variables x, y) satisfies a linear functional equation encoding the step-by-step description of walks. For instance, for the square lattice walks starting from the origin this equation reads {\$}{\$}{\backslash}left( {\{}xy - t(x + y + {\{}x^2{\}}y + x{\{}y^2{\}}){\}} {\backslash}right) {\{}{\backslash}text{\{}Q(x,y;t){\}}{\}} {\{}{\backslash}text{\{} = {\}}{\}} {\{}{\backslash}text{\{}xy - xtQ(x,0;t) - ytQ(0,y;t){\}}{\}}{\{}{\backslash}text{\{}.{\}}{\}}{\$}{\$}",
  Address       = "Basel",
  BookTitle     = "Mathematics and Computer Science II",
  date-added    = "2023-08-26 08:52:01 +0200",
  date-modified = "2023-08-26 09:09:51 +0200",
  ISBN          = "978-3-0348-8211-8",
  Pages         = "49--67",
  Publisher     = {Birkh{\"a}user Basel},
  Title         = "Counting Walks in the Quarter Plane",
  Year          = "2002",
  File          = "Counting Walks in the Quarter Plane.pdf"
}

@InProceedings{ BousquetMelou:2002, Author = "Bousquet-M{\'e}lou, Mireille", Editor = "Chauvin, Brigitte and Flajolet, Philippe and Gardy, Dani{`e}le and Mokkadem, Abdelkader", Abstract = "We study planar walks that start from a given point (i0j0), take their steps in a finite set {\$}{\$}{\backslash}mathfrak{{}S{}}{\$}{\$}, and are confined in the first quadrant x ≥ 0, y ≥ 0. Their enumeration can be attacked in a systematic way: the generating function Q(x, y; t) that counts them by their length (variable t) and the coordinates of their endpoint (variables x, y) satisfies a linear functional equation encoding the step-by-step description of walks. For instance, for the square lattice walks starting from the origin this equation reads {\$}{\$}{\backslash}left( {{}xy - t(x + y + {{}x^2{}}y + x{{}y^2{}}){}} {\backslash}right) {{}{\backslash}text{{}Q(x,y;t){}}{}} {{}{\backslash}text{{} = {}}{}} {{}{\backslash}text{{}xy - xtQ(x,0;t) - ytQ(0,y;t){}}{}}{{}{\backslash}text{{}.{}}{}}{\$}{\$}", Address = "Basel", BookTitle = "Mathematics and Computer Science II", date-added = "2023-08-26 08:52:01 +0200", date-modified = "2023-08-26 09:09:51 +0200", ISBN = "978-3-0348-8211-8", Pages = "49--67", Publisher = {Birkh{\"a}user Basel}, Title = "Counting Walks in the Quarter Plane", Year = "2002", File = "Counting Walks in the Quarter Plane.pdf" }