Abstract
We consider lattice paths with arbitrary step sizes, called generalized lattice paths, and we enumerate them with respect to string types of dpuqdr for any positive integers p,q, and r. We find that both numbers of types dpudr and dpu2+dr are independent of the number of i flaws for 1≤i≤n−1, i.e., they satisfy the Chung–Feller property, where u is a unit step, uk is an up step of length k, and u2+=us1us2⋯ust with ∑i=1tsi≥2. The enumeration of generalized lattice paths by peaks and by ascents is also studied.
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