A combinatorial study of the growing altitude elementary paths of the plane lattice Z²

Abstract

In this work we prove that a relationship exists between the elementary paths of the plane lattice Z² and those with growing altitude. Fortunately it is possible to make a more complete combinatorial study of the Z² growing altitude elementary paths and in particular those with barrier. From this combinatorial study we have established an important relationship permitting the calculation of the number of growing altitude elementary paths with barrier and of given length.

Citation

Dachraoui, T., Cherruault, Y. and Reiss, C. (1998), "A combinatorial study of the growing altitude elementary paths of the plane lattice Z²", Kybernetes, Vol. 27 No. 5, pp. 553-562. https://doi.org/10.1108/03684929810221582