The parallel TASEP, fixed particle number and weighted Motzkin paths
نویسندگان
چکیده
منابع مشابه
The parallel TASEP, fixed particle number and weighted Motzkin paths
In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size L is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with N particles is given. Further an interpretation in terms of (u, l, d)-colored weighted Motzkin paths is presented. Using previous results (Woelki and Sch...
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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...
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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 ...
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
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2013
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/46/50/505003