Louis W. Shapiro

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We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 4, 4, . . .) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving a bijection between weighted partial Motzkin paths with an elevation line and weighted free Motzkin paths, we find a matrix identity on the number of weighted(More)