Moments of m-step random walks in d=2 and d=4 equal the number of 2n-step lattice paths in dimension m-1, established via a bijection between Dyck paths with prescribed peaks and certain words.
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Brick Wall Excursions: Combinatorial Interpretation of Random Flight Moments
Moments of m-step random walks in d=2 and d=4 equal the number of 2n-step lattice paths in dimension m-1, established via a bijection between Dyck paths with prescribed peaks and certain words.