1974, Popular lectures in mathematics., ISBN 0226843165, vii, 35

Book

Theoretical computer science, ISSN 0304-3975, 2019, Volume 758, pp. 42 - 60

We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words...

Binomial coefficients of words | Bertrand numeration systems | Generalized Pascal triangles | Parry numbers | Perron numbers | β-expansions | COEFFICIENTS | COMPUTER SCIENCE, THEORY & METHODS | beta-expansions

Binomial coefficients of words | Bertrand numeration systems | Generalized Pascal triangles | Parry numbers | Perron numbers | β-expansions | COEFFICIENTS | COMPUTER SCIENCE, THEORY & METHODS | beta-expansions

Journal Article

Wireless Networks, ISSN 1022-0038, 10/2016, Volume 22, Issue 7, pp. 2221 - 2238

This paper introduces a Pascal’s triangle model to draw the potential locations and their probabilities for a normal node given the hop counts to the anchors according to the extent of detour of the shortest paths...

Engineering | Anisotropic networks | Distance estimation | Hop count | Communications Engineering, Networks | IT in Business | Computer Communication Networks | Electrical Engineering | Range-free localization | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | ERROR | TELECOMMUNICATIONS | SENSOR NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | Location-based systems | Algorithms | Mobile communication systems | Wireless communication systems | Research | Engineering research | Studies | Sensors | Wireless networks | Localization | Analysis | Anchors | Pascal (programming language) | Anisotropy | Position (location) | Matlab

Engineering | Anisotropic networks | Distance estimation | Hop count | Communications Engineering, Networks | IT in Business | Computer Communication Networks | Electrical Engineering | Range-free localization | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | ERROR | TELECOMMUNICATIONS | SENSOR NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | Location-based systems | Algorithms | Mobile communication systems | Wireless communication systems | Research | Engineering research | Studies | Sensors | Wireless networks | Localization | Analysis | Anchors | Pascal (programming language) | Anisotropy | Position (location) | Matlab

Journal Article

Fractals, ISSN 0218-348X, 10/2018, Volume 26, Issue 5, p. 1850071

We consider Pascal’s Triangle r mod p to be the entries of Pascal’s Triangle that are congruent to r mod p...

Article | Pascal's Triangle | Fractal | Hausdorff Metric | Box-Counting Dimension | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES

Article | Pascal's Triangle | Fractal | Hausdorff Metric | Box-Counting Dimension | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES

Journal Article

Fractals, ISSN 0218-348X, 09/2019, Volume 27, Issue 6, p. 1950098

When the entries of Pascal’s triangle which are congruent to a given nonzero residue modulo a fixed prime are mapped to corresponding locations of the unit square, a fractal-like structure emerges...

Frequency Analysis | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Pascal's Triangle | Fractal | MULTIDISCIPLINARY SCIENCES | Box-Counting Dimension

Frequency Analysis | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Pascal's Triangle | Fractal | MULTIDISCIPLINARY SCIENCES | Box-Counting Dimension

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 03/2019, Volume 26, Issue 1

We show that the n'th diagonal sum of Barry's modified Pascal triangle can be described as the continuant of the run lengths of the binary representation of n...

MATHEMATICS | continuant | MATHEMATICS, APPLIED | modified Pascal triangle | continued fraction | Stern's diatomic sequence

MATHEMATICS | continuant | MATHEMATICS, APPLIED | modified Pascal triangle | continued fraction | Stern's diatomic sequence

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 09/2016, Volume 80, pp. 24 - 47

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words...

MATHEMATICS, APPLIED | THEOREM | SYSTEMS

MATHEMATICS, APPLIED | THEOREM | SYSTEMS

Journal Article

1992, ISBN 0534161774, 609

Book

Optik, ISSN 0030-4026, 04/2018, Volume 159, pp. 14 - 20

In this paper a new method to construct zero cross correlation code with the help of Pascal's triangle pattern called Pascal's Triangle Matrix Code (PTMC...

Pascal's triangle | ZCC code | PIIN | MAI | OCDMA | LOCAL-AREA | CONSTRUCTION | OPTICS | FIBER NETWORKS

Pascal's triangle | ZCC code | PIIN | MAI | OCDMA | LOCAL-AREA | CONSTRUCTION | OPTICS | FIBER NETWORKS

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 10/2016, Volume 54, pp. 349 - 354

Let {0=w0 boolean Pascal triangles | Steinhaus triangles | weights of triangles | balanced Steinhaus triangles | 05 Combinatorics | Combinacions (Matemàtica) | 05A Enumerative combinatorics | Matemàtica discreta | Classificació AMS | Anells booleans | Combinatòria | Àlgebra | Anells i àlgebres | Matemàtiques i estadística | 06E Boolean algebras (Boolean rings) | 06 Order, lattices, ordered algebraic structures | Algebra, Boolean | Combinatorial analysis | Àrees temàtiques de la UPC

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 03/2018, Volume 26, Issue 1, pp. 189 - 203

In this paper, we describe a method to determine the power sum of the elements of the rows in the hyperbolic Pascal triangles corresponding to –4, q} with q ≥ 5...

Primary 05A10 | Secondary 11B65 | Binomial coefficients | Hyperbolic Pascal triangle | Power sum | 11B99 | Pascal triangle | MATHEMATICS | MATHEMATICS, APPLIED | RECURRENCES

Primary 05A10 | Secondary 11B65 | Binomial coefficients | Hyperbolic Pascal triangle | Power sum | 11B99 | Pascal triangle | MATHEMATICS | MATHEMATICS, APPLIED | RECURRENCES

Journal Article

2011, ISBN 0199742944, xvi, 421

Book

14.
Full Text
Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities

Mathematica Slovaca, ISSN 0139-9918, 4/2014, Volume 64, Issue 2, pp. 287 - 300

Our main purpose is to describe the recurrence relation associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle...

Algebra | linear recurrences | Mathematics, general | Mathematics | Primary 11B39, 05A19, 11A55, 05A10, 11B65, 05A15 | combinatorial properties | Pascal triangles | MATHEMATICS | CHEBYSHEV

Algebra | linear recurrences | Mathematics, general | Mathematics | Primary 11B39, 05A19, 11A55, 05A10, 11B65, 05A15 | combinatorial properties | Pascal triangles | MATHEMATICS | CHEBYSHEV

Journal Article

Signal, Image and Video Processing, ISSN 1863-1703, 1/2013, Volume 7, Issue 1, pp. 173 - 188

The aim of this paper is to provide a historical perspective of Tartaglia-Pascal’s triangle with its relations to physics, finance, and statistical signal processing...

Black–Scholes equation | Heat equation | Signal, Image and Speech Processing | Fibonacci sequence | Probability theory | Computer Imaging, Vision, Pattern Recognition and Graphics | Multimedia Information Systems | Fokker-Planck equation | Stochastic filtering | Yang Hui triangle | Kushner equation | Schrödinger equation | Engineering | Newton binomial | Tartaglia-Pascal triangle | Image Processing and Computer Vision | Black-Scholes equation | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Schrodinger equation

Black–Scholes equation | Heat equation | Signal, Image and Speech Processing | Fibonacci sequence | Probability theory | Computer Imaging, Vision, Pattern Recognition and Graphics | Multimedia Information Systems | Fokker-Planck equation | Stochastic filtering | Yang Hui triangle | Kushner equation | Schrödinger equation | Engineering | Newton binomial | Tartaglia-Pascal triangle | Image Processing and Computer Vision | Black-Scholes equation | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Schrodinger equation

Journal Article

Acta Universitatis Sapientiae, Mathematica, ISSN 1844-6094, 12/2017, Volume 9, Issue 2, pp. 336 - 347

The hyperbolic Pascal triangle (q 5) is a new mathematical construction, which is a geometrical generalization...

hyperbolic Pascal triangle | 11B39 | Fibonacci word | 05B30 | Hyperbolic Pascal triangle

hyperbolic Pascal triangle | 11B39 | Fibonacci word | 05B30 | Hyperbolic Pascal triangle

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 1/2013, Volume 169, Issue 1, pp. 1 - 14

...Monatsh Math (2013) 169:1–14 DOI 10.1007/s00605-012-0394-9 A discrete fractal in Z related to Pascal’s triangle modulo 2 Kevin D. Adams · Nicholas G. Foil...

Hausdorff dimension | Fractal | Binomial coefficients | Pascal’s triangle | Kummer’s theorem | Packing dimension | 11B65 | 28A80 | Mathematics, general | Mathematics | Fibonacci numbers | Self-similarity | Pascal's triangle | MATHEMATICS | PRIME | Kummer's theorem | DIMENSION

Hausdorff dimension | Fractal | Binomial coefficients | Pascal’s triangle | Kummer’s theorem | Packing dimension | 11B65 | 28A80 | Mathematics, general | Mathematics | Fibonacci numbers | Self-similarity | Pascal's triangle | MATHEMATICS | PRIME | Kummer's theorem | DIMENSION

Journal Article

Angewandte Chemie International Edition, ISSN 1433-7851, 06/2020, Volume 59, Issue 24, pp. 9617 - 9623

A protein Pascal triangle has been constructed as new type of supramolecular architecture by using the inducing ligand strategy that we previously developed for protein assemblies...

self-assembly | pascal triangle | wheat germ agglutinin | inducing ligand | SIALOGLYCOPEPTIDE | DESIGN | COMPLEX | SIERPINSKI-TRIANGLE | NANOSTRUCTURES | WHEAT-GERM-AGGLUTININ | CHEMISTRY, MULTIDISCIPLINARY | FRACTALS | CONSTRUCTION | POLYMER | CRYSTALS | Carbohydrates | Interlayers | Triangles | Mathematics | Proteins | Fabrication | Nanofabrication | Strategy | Ligands | Assemblies | Dimerization | Binding sites | Crystal structure

self-assembly | pascal triangle | wheat germ agglutinin | inducing ligand | SIALOGLYCOPEPTIDE | DESIGN | COMPLEX | SIERPINSKI-TRIANGLE | NANOSTRUCTURES | WHEAT-GERM-AGGLUTININ | CHEMISTRY, MULTIDISCIPLINARY | FRACTALS | CONSTRUCTION | POLYMER | CRYSTALS | Carbohydrates | Interlayers | Triangles | Mathematics | Proteins | Fabrication | Nanofabrication | Strategy | Ligands | Assemblies | Dimerization | Binding sites | Crystal structure

Journal Article

Inorganic Materials: Applied Research, ISSN 2075-1133, 7/2017, Volume 8, Issue 4, pp. 509 - 514

This article describes the application of the generalized Pascal triangle for description of fixed variation of the oscillation amplitude of friction force upon frictional interaction of materials...

Chemistry | Materials Science, general | generalized Pascal triangle | wear | simulation of friction | Inorganic Chemistry | Industrial Chemistry/Chemical Engineering | frictional indication of materials | oscillations of friction forces | Pascal's triangle | Usage | Models | Mathematical models | Friction | Oscillation

Chemistry | Materials Science, general | generalized Pascal triangle | wear | simulation of friction | Inorganic Chemistry | Industrial Chemistry/Chemical Engineering | frictional indication of materials | oscillations of friction forces | Pascal's triangle | Usage | Models | Mathematical models | Friction | Oscillation

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 273, pp. 453 - 464

In this paper, we introduce a new generalization of Pascal’s triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane...

Pascal triangle | Hyperbolic planar tessellations | Regular mosaics on hyperbolic plane | MATHEMATICS, APPLIED

Pascal triangle | Hyperbolic planar tessellations | Regular mosaics on hyperbolic plane | MATHEMATICS, APPLIED

Journal Article

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