Hiking a generalized Dyck path: A tractable way of calculating multimode boson evolution operators
نویسندگان
چکیده
منابع مشابه
Dyck path statistics
A wide range of articles dealing with the occurrence of strings in Dyck paths appear frequently in the literature [2], [3], [5], [6], [7] and [11]. A Dyck path of semilength n is a lattice path of N2 running from (0, 0) to (2n, 0), whose allowed steps are the up diagonal step (1, 1) and the down diagonal step (1,−1). These steps are called rise and fall respectively. It is clear that each Dyck ...
متن کاملLexicographical Generation of a Generalized Dyck Language
Given two disjoint alphabets T and T ] and a relation R T T ] , the generalized Dyck language D R over T T ] consists of all words w 2 (T T ]) ? which are equivalent to the empty word " under the congruence deened by x y " mod for all (x; y) 2 R. In this paper we present an algorithm that generates all words of length 2n of the generalized Dyck language lexicograph-ically. Thereby, each Dyck wo...
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A calculational derivation is given of an abstract path algorithm, one instance of the algorithm being Dijkstra's shortest-path algorithm, another being breadth-rst/depth-rst search of a directed graph. The basis for the derivation is the algebra of regular languages. Given is a (non-empty) set N and a j N j j N j matrix A, the rows and columns of which are indexed by elements of N. It is assum...
متن کاملOn Generalized Dyck Paths
We generalize the elegant bijective proof of the Chung Feller theorem from the paper of Young-Ming Chen [The Chung-Feller theorem revisited, Disc. Math. 308 (2008), 1328–1329].
متن کاملCounting Generalized Dyck Paths
The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...
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ژورنال
عنوان ژورنال: Computer Physics Communications
سال: 2015
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2015.05.020