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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 631 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
Meanders and Motzkin Words
 J. INTEGER SEQ
, 2004
"... We study the construction of closed meanders and systems of closed meanders, using Motzkin words with four letters. These words are generated by applying binary operation on the set of Dyck words. The procedure is based on the various kinds of intersection of the meandric curve with the horizonta ..."
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Cited by 8 (0 self)
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We study the construction of closed meanders and systems of closed meanders, using Motzkin words with four letters. These words are generated by applying binary operation on the set of Dyck words. The procedure is based on the various kinds of intersection of the meandric curve with the horizontal line.
A growth model for rna secondary structures
 Journal of Statistical Mechanics: Theory and Experiment
"... Abstract. A hierarchical model for the growth of planar arch structures for RNA secondary structures is presented, and shown to be equivalent to a treegrowth model. Both models can be solved analytically, giving access to scaling functions for large molecules, and corrections to scaling, checked by ..."
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Cited by 7 (2 self)
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Abstract. A hierarchical model for the growth of planar arch structures for RNA secondary structures is presented, and shown to be equivalent to a treegrowth model. Both models can be solved analytically, giving access to scaling functions for large molecules, and corrections to scaling, checked by numerical simulations of up to 6500 bases. The equivalence of both models should be helpful in understanding more general treegrowth processes. PACS numbers: 87.14.gn, 87.15.bd, 02.10.Ox, 02.50.EyA growth model for RNA secondary structures 2 1.
SPhT/96008 Meanders and the TemperleyLieb algebra
, 1996
"... The statistics of meanders is studied in connection with the TemperleyLieb algebra. Each (multicomponent) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram ma ..."
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The statistics of meanders is studied in connection with the TemperleyLieb algebra. Each (multicomponent) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of q, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks. * emails:
UNCCH/1996 Meander Determinants
, 1996
"... We prove a determinantal formula for quantities related to the problem of enumeration of (semi) meanders, namely the topologically inequivalent planar configurations of nonselfintersecting loops crossing a given (half) line through a given number of points. This is done by the explicit GramSchmi ..."
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We prove a determinantal formula for quantities related to the problem of enumeration of (semi) meanders, namely the topologically inequivalent planar configurations of nonselfintersecting loops crossing a given (half) line through a given number of points. This is done by the explicit GramSchmidt orthogonalization of certain bases of subspaces of the TemperleyLieb algebra. 11/96 The meander problem consists in counting the number Mn of meanders of order n, i.e. of inequivalent configurations of a closed nonselfintersecting loop crossing an infinite line through 2n points. The infinite line may be viewed as a river flowing from east to west, and the loop as a closed circuit crossing this river through 2n bridges, hence the name
SPhT/96062 Meanders: A Direct Enumeration Approach
, 1996
"... We study the statistics of semimeanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n = 29, we perform on the one hand a larg ..."
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We study the statistics of semimeanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n = 29, we perform on the one hand a large n extrapolation and on the other hand we reformulate the available data into a large q expansion, where q is a weight attached to each road. We predict a transition at q = 2 between a lowq regime with irrelevant winding, and a largeq regime with relevant winding. 06/96 * emails:
(1,2) (2,1) (1,2)
, 1997
"... Fig. 1: A sample walk diagram of order 10.(1,1) Fig. 2: The simplex Π+. The three oriented links correspond respectively to ǫ1 (right), ǫ2 (up, left) and ǫ3 (down, left). We have also indicated the origin (1, 1).(2,2) (2,1) (1,2) (2,1) ..."
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Fig. 1: A sample walk diagram of order 10.(1,1) Fig. 2: The simplex Π+. The three oriented links correspond respectively to ǫ1 (right), ǫ2 (up, left) and ǫ3 (down, left). We have also indicated the origin (1, 1).(2,2) (2,1) (1,2) (2,1)
Phase transitions and random matrices
, 2000
"... Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models. In this paper a brief review of phase transitions in invar ..."
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Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models. In this paper a brief review of phase transitions in invariant ensembles is provided, with some comments to the singular values decomposition in complex nonhermitian ensembles.