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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_1969_110_x,
     author = {Goodman, E. and Narayana, T.V.},
     title = {Lattice {Paths} with {Diagonal} {Steps}},
     journal = {Canadian mathematical bulletin},
     pages = {847--855},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-110-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-110-x/}
}
TY  - JOUR
AU  - Goodman, E.
AU  - Narayana, T.V.
TI  - Lattice Paths with Diagonal Steps
JO  - Canadian mathematical bulletin
PY  - 1969
SP  - 847
EP  - 855
VL  - 12
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-110-x/
DO  - 10.4153/CMB-1969-110-x
ID  - 10_4153_CMB_1969_110_x
ER  - 
%0 Journal Article
%A Goodman, E.
%A Narayana, T.V.
%T Lattice Paths with Diagonal Steps
%J Canadian mathematical bulletin
%D 1969
%P 847-855
%V 12
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-110-x/
%R 10.4153/CMB-1969-110-x
%F 10_4153_CMB_1969_110_x

[1] 1. Feller, W., An introduction to probability theory and its applications. (J. Wiley, New York, 1957). Google Scholar

[2] 2. Grossman, H.D., Fun with lattice points. Scripta Mathematica 15 (1949) 79–81. Google Scholar

[3] 3. Mohanty, S.G. and Handa, B.R., On lattice paths with several diagonal steps. Can. Math. Bull. 11 (1968) 537–545. Google Scholar

[4] 4. Moser, L. and Zayachkowski, W., Lattice paths with diagonal steps. Scripta Mathematica 26 (1961) 223–229. Google Scholar

[5] 5. Narayana, T. V., A problem in the theory of probability. J. Indian Soc. Agric. Statist. 6 (1954) 139–148. Google Scholar

[6] 6. Narayana, T.V., Sur les Treillis Formés par les Partitions d′un Entier et Leurs Applications à la Théorie des Probabilités. Comptes Rendus des Séances de l′Académie des Sciences, Paris, t. 240 (1955) 1188–1189. Google Scholar

[7] 7. Narayana, T.V., A partial order and its application to probability theory. Sankhyā: The Indian Journal of Statistics, 21 (1959) 91. Google Scholar

[8] 8. Narayana, T. V., An analogue of the multinomial theorem. Can. Math. Bull. 5 (1962) 43–50. Google Scholar

[9] 9. Poincaré, H., Calcul des Probabilités. (Gauthier Villars, Paris, 1913). Google Scholar

[10] 10. Rohatgi, V.K., A note on lattice paths with diagonal steps. Can. Math. Bull. 7 (1964) 470–472. Google Scholar

[11] 11. Stocks, D.R. Jr, Lattice paths in E3 with diagonal steps. Can. Math. Bull. 10 (1967) 653–658. Google Scholar

Cité par Sources :