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Equations with a dyck language solution

1976
*
Information and Control
*

In cases where the

doi:10.1016/s0019-9958(76)90436-8
fatcat:5yxzrqg2obbcxikkxq7napte2u
*solutions*are unique these may be represented in terms of*Dyck**languages*. We will also discuss*equations**with*nonunique*solutions*. 1. PRELIMINARIES 1.1. ... In this paper we consider*languages*which are*solutions*of*equations*of the type X = XAiXBiX 4-"" + XA~XB~X + L a . ... In Sections 3 and 4 we consider*equations**with*nonunique*solutions*. 1.2. ...##
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Enumeration of polyominoes using Macsyma

1991
*
Theoretical Computer Science
*

This paper shows the use of a symbolic

doi:10.1016/0304-3975(91)90152-r
fatcat:ihw3prbh3zasng2ujpjybavozm
*language*, Macsyma, to obtain new exact or asymptotic results il; combinatorics. The examples are taken among poiyominoes objects. ... Appendix 11 We give in the following a system of*equations*allowing the generation of the pigmented*Dyck**language*defined in [9]. e denote by D the classical*Dyck**language*. ... The letter R means that the woi-ds of the associated*language*to the non-terminal are prime*Dyck*words shuffled*with*letters "a". The non-terminal PP is associated to the pigmented*Dyck**language*. ...##
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On the enumeration and generation of generalized Dyck words

2000
*
Discrete Mathematics
*

A random generation scheme is shown for generalized

doi:10.1016/s0012-365x(00)00150-3
fatcat:7qa3fbqievbyffmwhz3tfdgymm
*Dyck**languages*, which leads to some asymptotic results. ... We provide a new algebraic grammar for generalized*Dyck**languages*as introduced by Labelle and Yeh (Discrete Math. 82 (1990) 1-6). ... Acknowledgements We would like to thank Mireille Bousquet-MÃ elou for pointing to us the right use of the Lagrange inversion formula, which lead to the enumeration formula for 3 2 -*Dyck*paths. ...##
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Page 565 of Mathematical Reviews Vol. 58, Issue 1
[page]

1979
*
Mathematical Reviews
*

Representations of the

*Dyck**languages*using only*language*-theo- retic operations are given. ... Branislav Rovan (Bratislava) 58 #3747 Ruohonen, Keijo A note on*language**equations*involving morphisms. Inform. Process. Lett. 7 (1978), no. 5, 209-212. ...##
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A note on the iteration of infinite matrices

1988
*
RAIRO - Theoretical Informatics and Applications
*

Assume that seR is a

doi:10.1051/ita/1988220201631
fatcat:5rd47rxqw5azncgh2gwfk4kykq
*solution*of the*équation*x -a + r.x for a,reR, that means s = a + r.s. Then r* exists and s = r*,a holds. ... Latter on we will see that 93* exists and its coefficient at the place (0,0) equals the*Dyck**language*of order 1*with*a and a as generators. • ITERATION OF INFINITE MATRICES A semiring R is called itérative ... ., a k , then the*solution*of the*équation*(*) equals the*Dyck**languages*of order k {cf. [1] ). ...##
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Zeta functions and topological entropy of the Markov-Dyck shifts
[article]

2007
*
arXiv
*
pre-print

The Markov-

arXiv:0706.3262v1
fatcat:oyokjrefxfhzjo33rm5qhh6zhm
*Dyck*shifts arise from finite directed graphs. An expression for the zeta function of a Markov-*Dyck*shift is given. The derivation of this expression is based on a formula in Keller (G. ... For a class of examples that includes the Fibonacci-*Dyck*shift the zeta functions and topological entropy ae determined. ...*Equation*(4.23) is a multiple of*equation*(4.21) precisely if c = a + b and z = 1 1+a+b , and from this one sees, consulting (4.24), that both*solutions*of*equation*(4.21) are also*solutions*of*equation*...##
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A characterization of poly-slender context-free languages

2000
*
RAIRO - Theoretical Informatics and Applications
*

We give a precise characterization of the kpoly-slender context-free

doi:10.1051/ita:2000100
fatcat:u5cp7v5dancjvn6hw2rsdhf6wa
*languages*. The well-known characterization of the k-poly-slender regular*languages*is an immediate consequence of ours. ... For a non-negative integer k, we say that a*language*L is k-poly-slender if the number of words of length n in L is of order O(n k ). ... Let us consider a context-free*language*L which is k-poly-slender. Then, by Theorem 6, L is a nite union of*Dyck*loops. If L contains no l-*Dyck*loop*with*l > k + 1, then we are done. ...##
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Algebraic languages and polyominoes enumeration

1984
*
Theoretical Computer Science
*

The unique

doi:10.1016/0304-3975(84)90116-6
fatcat:r7db4tihprfr5geedwhrww3l7q
*solution*of the system contains the (noncommutative) generating function t = C H,E L w of the*language*L. ... By constructing a bijection between convex polyominoes and words of an algebraic*language*, atjd bq solving the corresponding algebraic qstem, we proie that the number of convex polyominoes*with*perimeter ... of*equations*, in term of the generating function c(t) of the*Dyck**language*. ...##
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Unary multiple equality sets: The languages of rational matrices

1981
*
Information and Control
*

Finally crossing-free unary multiple equality sets are introduced, which vary from unary multiple equality sets in a similar way as the one-sided

doi:10.1016/s0019-9958(81)90335-1
fatcat:xwgspui4avfvnpfnhk46wc2r7m
*Dyck*set varies from the two-sided*Dyck*set. ... These*languages*can equally well be defined by rational matrices. Unary multiple equality sets have extraordinary*language*theoretic properties. ... In a very natural way unary multiple equality sets can be associated*with*the sets of nonnegative integral*solutions*of systems of linear*equations*. ...##
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New Formulas for Dyck Paths in a Rectangle
[article]

2015
*
arXiv
*
pre-print

By using Ferrers diagrams associated to

arXiv:1509.07832v1
fatcat:erinsx2cm5gybjllxtm4zw2q2m
*Dyck*paths, we derive formulas for the enumeration of D_a,b*with*a and b non relatively prime, in terms of Catalan numbers. ... They are a natural generalization of the classical*Dyck*words enumerated by the Catalan numbers. ... It is well-known that the*language*of*Dyck*words on Σ = {0, 1} is the*language*generated by the algebraic grammar D → 0D1D + ε. ...##
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Page 794 of Mathematical Reviews Vol. 49, Issue 2
[page]

1975
*
Mathematical Reviews
*

It is shown that the parallel context-free

*languages*are incomparable*with*the context-free*languages*(CFL) (ef. the example given above, and a direct proof is given that | the*Dyck**language*is not PCL ... The author points out that a context-free*language*can be viewed as the minimal*solution*of a finite system of*equations*EH, of the form X,=f,(Xo, ---, X,, Yo, «++, Ym), where the X,, Y, range over subsets ...##
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Page 5455 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

A. (2-KIEV)
Minimal elements of Church-Rosser systems

*with*respect to formal*languages*. ... Summary: “The aim of this paper is to study the properties of*languages*generated by shuffle expressions*with*no ®@ operator nested. ...##
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Two combinatorial statistics on Dyck paths

1995
*
Discrete Mathematics
*

, Universit6 Bordeaux I, and

doi:10.1016/0012-365x(93)e0147-v
fatcat:2dntsivzg5gu5lsckove2ml6ka
*with*partial support from NSF grant DMS-9108749. 0012-365X/95/$09.50 C(C) 1995--Elsevier Science B.V. ... All rights reserved SSDI 0012-365X(93)E0147-V Definitions, notation, and preliminary results*Dyck*paths, pyramid weight, and exterior pairs A*Dyck*path is a path in the first quadrant, which begins at ... The reader will recognize the source of these*equations*: the second*equation*describes the*Dyck*paths of pyramid weight k > 0 via their unique factorization p=p'p"*with*p' being the maximal left primitive ...##
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Recursive Prime Factorizations: Dyck Words as Numbers
[article]

2021
*
arXiv
*
pre-print

*Dyck*

*language*represents a number. ... I propose a class of numeral systems where numbers are represented by

*Dyck*words,

*with*the systems arising from a generalization of prime factorization. ...

*Dyck*

*language*. ...

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Attribute grammars are useful for combinatorics

1992
*
Theoretical Computer Science
*

The peaks (troughs) of a

doi:10.1016/0304-3975(92)90380-x
fatcat:eezr7g6pyraitoxz2uvceo5ita
*Dyck*path correspond*with*the factors xx (xx) of the associated*Dyck*word. _I_ I -I_ _l _ l_ _I W(P)=S'(P) -_-_ -Fig. 5. ... Expanding the analytic*solution*of the previous*equation*shows that C, Definiton 3. 2 . 2 The q-analog of the generating function L(G) (denoted by 4L) is defined by qL = y& (w 4). ...
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