scholarly journals New Analogues of the Pascal Triangle and Electronic Clouds in Atom

2018 ◽  
Vol 1 (3) ◽  
Author(s):  
Alexander Urkin
Keyword(s):  
Pascal Triangle

PENERAPAN METODE SEGITIGA PASCAL ALJABAR UNTUK MEMAKSIMALKAN TEKNIK PENYANDIAN ALGORITMA WORD AUTO KEY ENCRYPTION (WAKE)

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Kaldius Ndruru ◽  
Putri Ramadhani
Keyword(s):  
Data Security ◽  
Important Data ◽  
Pascal Triangle ◽  
Absolute Requirement ◽  
Cryptographic Algorithms ◽  
Secure Data ◽  
Triangle Method ◽  
Symmetric Key

Security of data stored on computers is now an absolute requirement, because every data has a high enough value for the user, reader and owner of the data itself. To prevent misuse of the data by other parties, data security is needed. Data security is the protection of data in a system against unauthorized authorization, modification, or destruction. The science that explains the ways of securing data is known as cryptography, while the steps in cryptography are called critical algorithms. At this time, there are many cryptographic algorithms whose keys are weak especially the symmetric key algorithm because they only have one key, the key for encryption is the same as the decryption key so it needs to be modified so that the cryptanalysts are confused in accessing important data. The cryptographic method of Word Auto Key Encryption (WAKE) is one method that has been used to secure data where in this case the writer wants to maximize the encryption key and description of the WAKE algorithm that has been processed through key formation. One way is to apply the algebraic pascal triangle method to maximize the encryption key and description of the WAKE algorithm, utilizing the numbers contained in the columns and rows of the pascal triangle to make shifts on the encryption key and the description of the WAKE algorithm.Keywords: Cryptography, WAKE, pascal

scholarly journals Computing support for testing equal values of the figurative numbers in the Pascal triangle

2020 ◽  
Vol 2 (7) ◽  
pp. 36-41
Author(s):  
Miroslava Mihajlov Carević ◽  
Miloš Ilić ◽  
Milena Petrović ◽  
Nebojša Denić
Keyword(s):  
Programming Language ◽  
Mathematical Analysis ◽  
Computer Laboratory ◽  
C Programming Language ◽  
Pascal Triangle ◽  
C Programming ◽  
Computing Support

In this paper we deal with a method for the determination of numbers in a Pascal triangle that are simultaneously triangular, tetrahedral and pentaedroidni. The collected results, obtained by mathematical analysis, were verified by computer. For this purpose, we used the C# programming language as well as the computer laboratory within our University in order to test the results. The results collected by computer confirmed the accuracy of the results obtained by mathematical analysis.

Preserving log-concavity for p,q-binomial coefficient

2019 ◽  
Vol 11 (02) ◽  
pp. 1950017
Author(s):  
Moussa Ahmia ◽  
Hacène Belbachir
Keyword(s):  
Binomial Coefficient ◽  
Binomial Coefficients ◽  
Linear Transformations ◽  
Pascal Triangle

We study the log-concavity of a sequence of [Formula: see text]-binomial coefficients located on a ray of the [Formula: see text]-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear transformations associated to [Formula: see text]-Pascal triangle.

scholarly journals Modified For The Pascal Triangle Multinomial

2019 ◽  
Vol 1387 ◽  
pp. 012145
Author(s):  
Media Rosha ◽  
Arnellis
Keyword(s):  
Pascal Triangle

scholarly journals -DEFORMED RATIONALS AND -CONTINUED FRACTIONS

2020 ◽  
Vol 8 ◽  
Author(s):  
SOPHIE MORIER-GENOUD ◽  
VALENTIN OVSIENKO
Keyword(s):  
Continued Fractions ◽  
Jones Polynomial ◽  
Total Positivity ◽  
Recursive Formula ◽  
Rational Numbers ◽  
Binomial Coefficients ◽  
Indecomposable Representation ◽  
Pascal Triangle ◽  
Rational Knots ◽  
Gaussian Binomial Coefficients

We introduce a notion of $q$ -deformed rational numbers and $q$ -deformed continued fractions. A $q$ -deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$ -deformed Pascal identity for the Gaussian binomial coefficients, but the Pascal triangle is replaced by the Farey graph. The coefficients of the polynomials defining the $q$ -rational count quiver subrepresentations of the maximal indecomposable representation of the graph dual to the triangulation. Several other properties, such as total positivity properties, $q$ -deformation of the Farey graph, matrix presentations and $q$ -continuants are given, as well as a relation to the Jones polynomial of rational knots.

Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle

2017 ◽  
Vol 27 (3) ◽  
Author(s):  
Fedor M. Malyshev
Keyword(s):  
Extreme Values ◽  
Pascal Triangle

AbstractThe paper is concerned with estimating the number

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