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Lattice paths, reflections, & dimension-changing bijections. (English) Zbl 0770.05003
Summary: We enumerate various families of planar lattice paths consisting of unit steps in directions N, S, E, or W, which do not cross the \(x\)-axis or both \(x\)- and \(y\)-axes. The proofs are purely combinatorial throughout, using either reflections or bijections between these NSEW-paths and linear NS-paths. We also consider other dimension-changing bijections.

MSC:
05A15 Exact enumeration problems, generating functions
05A10 Factorials, binomial coefficients, combinatorial functions
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