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Underdiagonal lattice paths with unrestricted steps. (English) Zbl 0923.05003
The paper studies a generalization of Dyck paths, i.e. lattice paths in the plane composed of a set of unrestricted steps. An algorithm is introduced to obtain the generating function for the number of underdiagonal paths for a large class of path problems. The techniques of the paper use previous work of M. P. Schützenberger [Inf. Control 6, 246-264 (1963; Zbl 0123.12502)] and J. R. Goldman [J. Comb. Theory, Ser. A 24, 318-338 (1978; Zbl 0411.05010)] for making combinatorial decomposition based on context-free grammar, in order to obtain a recurrence relation.

05A15 Exact enumeration problems, generating functions
Full Text: DOI
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