Matrix identities on weighted partial Motzkin paths
نویسندگان
چکیده
منابع مشابه
Matrix identities on weighted partial Motzkin paths
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 Motzkin paths and the sequence (1, k, ...
متن کاملIdentities from Weighted Motzkin Paths
Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find combinatorial interpretations of two identities related to the Narayana polynomials and the Catalan numbers. These interpretations answer two problems posed recently by Coker. AMS Classification: 05A15, 05A19
متن کاملIdentities from Weighted 2-Motzkin Paths
Based on a weighted version of the bijection between Dyck paths and 2-Motzkin paths, we find combinatorial interpretations of two identities related to the Narayana polynomials and the Catalan numbers, in answer to two problems recently proposed by Coker. AMS Classification: 05A15, 05A19
متن کاملWeighted 2-Motzkin Paths
This paper is motivated by two problems recently proposed by Coker on combinatorial identities related to the Narayana polynomials and the Catalan numbers. We find that a bijection of Chen, Deutsch and Elizalde can be used to provide combinatorial interpretations of the identities of Coker when it is applied to weighted plane trees. For the sake of presentation of our combinatorial corresponden...
متن کاملOn Computing the Total Displacement Number via Weighted Motzkin Paths
Counting the number of permutations of a given total displacement is equivalent to counting weighted Motzkin paths of a given area (Guay-Paquet and Petersen [10]). The former combinatorial problem is still open. In this work we show that this connection allows to construct efficient algorithms for counting and for sampling such permutations. These algorithms provide a tool to better understand ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.02.005