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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
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
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
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
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
Journal Article
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
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
Journal Article
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
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
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
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
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
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
Journal Article
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