Geodesic
Lattice Paths with Diagonal Steps
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 847-855

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The André-Poincaré "probléme du scrutin" [9] can be stated as follows: In an election between two candidates A polls m votes, B polls n, m > n. If the votes are counted one by one what is the probability that A leads B throughout the counting? Many derivations and interpretations of the solution have been given and a convenient summary of methods till 1956 can be found in Feller [1]. So numerous are the generalizations of ballot problems and their applications since this date that we do not even attempt an enumeration here. 
Goodman, E.; Narayana, T.V. Lattice Paths with Diagonal Steps. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 847-855. doi: 10.4153/CMB-1969-110-x
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     title = {Lattice {Paths} with {Diagonal} {Steps}},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
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     number = {6},
     doi = {10.4153/CMB-1969-110-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-110-x/}
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