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#A3 INTEGERS 13 (2013) COUNTING HERON TRIANGLES WITH CONSTRAINTS
"... Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed positiv ..."
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Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed
Wrap&Zip: Linear decoding of planar triangle graphs
, 1999
"... The Edgebreaker compression technique, introduced in [11], encodes any unlabeled triangulated planar graph of t triangles using a string of 2t bits. The string contains a sequence of t letters from the set {C, L, E, R, S} and 50% of these letters are C. Exploiting constraints on the sequence, we sho ..."
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Cited by 18 (2 self)
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The Edgebreaker compression technique, introduced in [11], encodes any unlabeled triangulated planar graph of t triangles using a string of 2t bits. The string contains a sequence of t letters from the set {C, L, E, R, S} and 50% of these letters are C. Exploiting constraints on the sequence, we
Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients
, 2010
"... We are interested in Fully Packed Loops in a triangle (TFPLs), as introduced by Caselli at al. and studied by Thapper. We show that for Fully Packed Loops with a fixed link pattern (refined FPL), there exist linear recurrence relations with coefficients computed from TFPL configurations. We then gi ..."
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Cited by 4 (2 self)
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then give constraints and enumeration results for certain classes of TFPL configurations. For special boundary conditions, we show that TFPLs are counted by the famous Littlewood Richardson coefficients.
Correlation decay and deterministic FPTAS for counting listcolorings of a graph
 In Proc. 18th ACMSIAM Symp. Discret. Algorithms (2007), SIAM
"... Abstract We propose a deterministic algorithm for approximately counting the number of list colorings of a graph. Under the assumption that the graph is triangle free, the size of every list is at least α∆, where α is an arbitrary constant bigger than α * * = 2.8432 . . ., the solution of αe − 1 α ..."
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Cited by 30 (9 self)
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Abstract We propose a deterministic algorithm for approximately counting the number of list colorings of a graph. Under the assumption that the graph is triangle free, the size of every list is at least α∆, where α is an arbitrary constant bigger than α * * = 2.8432 . . ., the solution of αe − 1 α
Constraints on Area Variables in Regge Calculus
, 2000
"... We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4sphere. The number of independent constraints on the variations of the triang ..."
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of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing these independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example. Area Regge calculus [1] is a
S (XX)00000 COUNTING CYCLES
, 1999
"... Abstract. We obtain sharp bounds for the number of ncycles in a finite graph G as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. i=1 xik, En route, we prove sharp estimates on both ∑ n i=1 xk i and ∑ n subject to the constraint ..."
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to the constraints that ∑ n i=1 x2 i = C and ∑ n i=1 xi = 0. This note has been inspired by the following question, which had been asked at the oral entrance exams (see [4]) to the Moscow State University Mathematics Department (MekhMat) to certain applicants: Question 1. Let G be a graph with E edges. Let
Rossignac&Szymczak Computational Geometry: Theory and Applications (5/2/99 11:42 AM) page 1 Edgebreaker compression and Wrap&Zip decoding of the connectivity of triangle meshes
"... The Edgebreaker compression, introduced by Rossignac in [13], encodes any unlabeled triangulated planar graph of t triangles using a CLERS string of 2t bits, which represents a sequence of t symbols from the set {C,L,E,R,S}. Exploiting constraints between consecutive symbols, the CLERS string may in ..."
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The Edgebreaker compression, introduced by Rossignac in [13], encodes any unlabeled triangulated planar graph of t triangles using a CLERS string of 2t bits, which represents a sequence of t symbols from the set {C,L,E,R,S}. Exploiting constraints between consecutive symbols, the CLERS string may
INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 18 (2001) L43–L47 www.iop.org/Journals/cq PII: S02649381(01)192890 LETTER TO THE EDITOR Constraints on area variables in Regge calculus
, 2000
"... We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4sphere. The number of independent constraints on the variations of the triang ..."
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of the triangle areas is shown to be equal to the difference between the numbers of triangles and edges. A general method of choosing these independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example. PACS number: 0460L Area
Draft version Preprint typeset using L ATEX style emulateapj v. 6/22/04 OPTIMAL CAPTURE OF NONGAUSSIANITY IN WEAK LENSING SURVEYS: POWER SPECTRUM,
, 909
"... We compare the efficiency of weak lensingselected galaxy clusters counts and of the weak lensing bispectrum at capturing nonGaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected cluste ..."
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function of clusters ’ mass and redshift. We show that when combined with the power spectrum, those four kinds of counts provide similar constraints, thus allowing one to perform the most direct counts, signaltonoise peaks counts, and get percent level constraints on cosmological parameters. We show
unknown title
, 2000
"... We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4sphere. The number of independent constraints on the variations of the triang ..."
Abstract
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of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing these independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example. Area Regge calculus [1] is a
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