# Lattice paths with a first return decomposition constrained by the maximal height of a pattern

@article{Baril2021LatticePW, title={Lattice paths with a first return decomposition constrained by the maximal height of a pattern}, author={Jean-Luc Baril and Sergey Kirgizov}, journal={ArXiv}, year={2021}, volume={abs/2110.02831} }

We consider the system of equations Ak(x) = p(x)Ak−1(x)(q(x) + ∑ k i=0 Ai(x)) for k > r+ 1 where Ai(x), 0 6 i 6 r, are some given functions and show how to obtain a close form for A(x) = ∑ k>0 Ak(x). We apply this general result to the enumeration of certain subsets of Dyck, Motzkin, skew Dyck, and skew Motzkin paths, defined recursively according to the first return decomposition with a monotonically non-increasing condition relative to the maximal ordinate reached by an occurrence of a given… Expand

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