Matrix Identities on Weighted Partial Motzkin Paths

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dc.creatorChen, William Y. C.
dc.creatorLi, Nelson Y.
dc.creatorShapiro, Louis W.
dc.creatorYan, Sherry H. F.
dc.date2005-09-12
dc.date.accessioned2026-07-07T05:23:08Z
dc.date.available2026-07-07T05:23:08Z
dc.descriptionWe give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence $(1, 4, 4^2, 4^3, ...)$ 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 Motzkin paths and the sequence $(1, k, k^2, k^3, ...)$ for any $k \geq 2$. By extending this argument to partial Motzkin paths with multiple elevation lines, we give a combinatorial proof of an identity recently obtained by Cameron and Nkwanta. A matrix identity on colored Dyck paths is also given, leading to a matrix identity for the sequence $(1, t^2+t, (t^2+t)^2, ...)$.
dc.description15 pages, 3figures
dc.identifierhttps://arxiv.org/abs/math/0509255
dc.identifierhttp://arxiv.org/abs/math/0509255
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76316
dc.subjectCombinatorics
dc.subject05A15, 05A19
dc.titleMatrix Identities on Weighted Partial Motzkin Paths
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