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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
Random incidence matrices: moments of the spectral density
 J. Stat. Phys
, 2001
"... We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices: any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large ..."
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Cited by 18 (3 self)
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We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices: any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large N and fixed p the spectrum contains a large eigenvalue at Np and a semicircle of “small ” eigenvalues. For large N and fixed average connectivity pN (dilute or sparse random matrices limit) we show that the spectrum always contains a discrete component. An anomaly in the spectrum near eigenvalue 0 for connectivity close to e is observed. We develop recursion relations to compute the moments as explicit polynomials in pN. Their growth is slow enough so that they determine the spectrum. The extension of our methods to the Laplacian matrix is given in Appendix.
Meanders: exact asymptotics
 Nuc. Phys. B
"... We conjecture that meanders are governed by the gravitational version of a c = −4 twodimensional conformal field theory, allowing for exact predictions for the meander configuration exponent α = √ 29 ( √ 29 + √ 5)/12, and the semimeander exponent ¯α = 1 + √ 11 ( √ 29 + √ 5)/24. This result foll ..."
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Cited by 4 (1 self)
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We conjecture that meanders are governed by the gravitational version of a c = −4 twodimensional conformal field theory, allowing for exact predictions for the meander configuration exponent α = √ 29 ( √ 29 + √ 5)/12, and the semimeander exponent ¯α = 1 + √ 11 ( √ 29 + √ 5)/24. This result follows from an interpretation of meanders as pairs of fully packed loops on a random surface, described by two c = −2 free fields. The above values agree with recent numerical estimates. We generalize these results to a score of meandric numbers with various geometries and arbitrary loop fugacities. 10/99 * emails:
A Fast Algorithm To Generate Open Meandric Systems and Meanders
"... An open meandric system is a planar configuration of acyclic curves crossing an infinite horizontal line in the plane such that the curves may extend in both horizontal directions. We present a fast, recursive algorithm to exhaustively generate open meandric systems with n crossings. We then illustr ..."
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Cited by 3 (3 self)
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An open meandric system is a planar configuration of acyclic curves crossing an infinite horizontal line in the plane such that the curves may extend in both horizontal directions. We present a fast, recursive algorithm to exhaustively generate open meandric systems with n crossings. We then illustrate how to modify the algorithm to generate unidirectional open meandric systems (the curves extend only to the right) and nonisomorphic open meandric systems where equivalence is taken under horizontal reflection. Each algorithm can be modified to generate systems with exactly k curves. In the unidirectional case when k=1, we can apply a minor modification along with some additional optimization steps to yield the first fast and simple algorithm to generate open meanders.
ON THE REPRESENTATION OF MEANDERS
"... ABSTRACT. We will introduce a new approach for studying plane meanders. The set of all meanders of order n possesses a natural order structure and forms a graded poset. We will show how these representations can be used to develop an efficient and very flexible construction algorithm and how to obta ..."
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ABSTRACT. We will introduce a new approach for studying plane meanders. The set of all meanders of order n possesses a natural order structure and forms a graded poset. We will show how these representations can be used to develop an efficient and very flexible construction algorithm and how to obtain counting formulae for meanders. 1.
Meanders and Stamp Foldings: Fast Generation Algorithms
, 2008
"... By considering a permutation representation for meanders, semimeanders, and stamp foldings we construct a new data structure that will allow us to extend the order of a given meander, semimeander, or stamp folding in constant time. Then using this data structure, we develop a constant amortized ti ..."
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By considering a permutation representation for meanders, semimeanders, and stamp foldings we construct a new data structure that will allow us to extend the order of a given meander, semimeander, or stamp folding in constant time. Then using this data structure, we develop a constant amortized time algorithm to generate all semimeanders of order n. By maintaining the windfactor for semimeanders and applying an additional optimization, the algorithm can be modified to produce the fastest known algorithm to generate meanders. Finally, by handling an additional special case, the semimeander algorithm can be modified to generate all stamp foldings of order n in constant amortized time.
Nonperturbative Quantum Effects 2000 PROCEEDINGS From FullyPacked Loops to Meanders: Exact Exponents
"... Abstract: We address the meander problem “enumerate all topologically inequivalent configurations of a closed nonselfintersecting plane curve intersecting a given line through a fixed number of points”. We show that meanders may be viewed as the configurations of a suitable fullypacked loop statist ..."
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Abstract: We address the meander problem “enumerate all topologically inequivalent configurations of a closed nonselfintersecting plane curve intersecting a given line through a fixed number of points”. We show that meanders may be viewed as the configurations of a suitable fullypacked loop statistical model defined on a random surface. Using standard results relating critical singularities of a lattice model to its gravitational version on random surfaces, we predict the meander configuration exponent α =(29+ √ 145)/12 and many other meandric exponents. 1.
PART A: FOLDING OF REGULAR LATTICES
, 2005
"... Geometrically constrained statistical systems on regular and random lattices: ..."
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Geometrically constrained statistical systems on regular and random lattices:
and
, 2000
"... Abstract: This note addresses the meander enumeration problem: “Count all topologically inequivalent configurations of a closed planar non selfintersecting curve crossing a line through a given number of points”. We review a description of meanders introduced recently in terms of the coupling to gr ..."
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Abstract: This note addresses the meander enumeration problem: “Count all topologically inequivalent configurations of a closed planar non selfintersecting curve crossing a line through a given number of points”. We review a description of meanders introduced recently in terms of the coupling to gravity of a twoflavored fullypacked loop model. The subsequent analytic predictions for various meandric configuration exponents are checked against exact enumeration, using a transfer matrix method, with an excellent agreement.