Generating functions for a lattice path model introduced by Deutsch

Abstract

The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size −3, −5, −7, . . . . For such paths, we find the generating functions of them, according to length, ending at level i, both, when considering them from left to right and from right to left. The generating functions are intrinsically cubic, and thus (for i = 0) in bijection to various objects, like even trees, ternary trees, etc.

Keywords

• deutsch paths
• cubic equation
• cramer's rule
• girard-waring formula
• 05a15
• 15b36
• 11c20