منابع مشابه
Bijective Recurrences concerning Schrr Oder Paths
Consider lattice paths in Z 2 with three step types: the up diagonal (1; 1), the down diagonal (1; ?1), and the double horizontal (2; 0). For n 1, let S n denote the set of such paths running from (0; 0) to (2n; 0) and remaining strictly above the x-axis except initially and terminally. It is well known that the cardinalities, r n = jS n j, are the large Schrr oder numbers. We use lattice paths...
متن کاملBijective Recurrences concerning Schro"der Paths
Consider lattice paths in Z2 with three step types: the up diagonal (1, 1), the down diagonal (1,−1), and the double horizontal (2, 0). For n ≥ 1, let Sn denote the set of such paths running from (0, 0) to (2n, 0) and remaining strictly above the x-axis except initially and terminally. It is well known that the cardinalities, rn = |Sn|, are the large Schröder numbers. We use lattice paths to in...
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We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. They are counted by the Motzkin numbers, related to the well known Catalan numbers. Associated with the Motzkin paths, we introduce the Motzkin polynomial, which is a multi-variable polynomial “counting” all Motzkin paths of a certain type. Motzkin polynomials (also called Jacobi-Rogers polynomials)...
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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...
متن کاملDyck paths , Motzkin paths and traffic jams
It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the asymmetric exclusion process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee–Yang theory of partition function zeros to ...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2001
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0753