Lattice Path-enumeration in a Cartesian Grid: Application to the Well Correlation Problem.

@inproceedings{Royer2GM2010,
 abstract = { A number of combinatorial problems lead to the evaluation of the number of paths starting from the lower left corner A of a regular grid with m × n square cells (i.e. m + 1 × n + 1 nodes), and finishing in the upper right corner B. The solution to this problem is well known when the paths consist entirely of edges pointing rightwards or upwards, and are defined along the edges of the grid (known as the Ballot problem). For grids with n×n square cells, monotonic paths are paths that do not pass above the diagonal. The number of monotonic paths is equal to the Catalan number Cn. The Catalan number can be related to the problem of estimating the number of different paths along a fracture network. If paths consist of edges pointing rightwards or upwards, or of diagonals pointing rightwards, the number of lattice paths is then the Delannoy number Dn,m . Some recursive expressions to compute Dn,m are given in this paper. The Delannoy number Dn,m is also the number of different ways to correlate laterally the stratigraphy observed along two wells in which m and n end-members have been observed, or in other words the number of possible connections between two wells.
The paper summarizes most of the results presently known on these combinatory problems and apply them to discuss the two and multi wells correlation problem. },
 author = { Royer, Jean-Jacques AND Lallier, Florent },
 booktitle = { Proc. 30th Gocad Meeting, Nancy },
 title = { Lattice Path-enumeration in a Cartesian Grid: Application to the Well Correlation Problem. },
 year = { 2010 }
}