scholarly journals Modified For The Pascal Triangle Multinomial

2019 ◽  
Vol 1387 ◽  
pp. 012145
Author(s):  
Media Rosha ◽  
Arnellis
Keyword(s):  
Author(s):  
Kaldius Ndruru ◽  
Putri Ramadhani

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


Author(s):  
Miroslava Mihajlov Carević ◽  
Miloš Ilić ◽  
Milena Petrović ◽  
Nebojša Denić

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.


2019 ◽  
Vol 11 (02) ◽  
pp. 1950017
Author(s):  
Moussa Ahmia ◽  
Hacène Belbachir

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.


2020 ◽  
Vol 8 ◽  
Author(s):  
SOPHIE MORIER-GENOUD ◽  
VALENTIN OVSIENKO

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.


2017 ◽  
Vol 27 (3) ◽  
Author(s):  
Fedor M. Malyshev

AbstractThe paper is concerned with estimating the number


1933 ◽  
Vol 26 (6) ◽  
pp. 382-384
Author(s):  
Vera Sanford

It is interesting that Jacques Bernoulli should have been born in the very year of the correspondence between Pascal and Fermat which laid the foundations of the study of probability, for Jacques Bernoulli's many important contributions to mathematics, perhaps the most significant was his Ars Conjectandi, published posthumously in 1713. This work contained the first use of the term “permutation”; the Pascal triangle, given as an original invention; and Bernoulli's Theorem which Todhunter said “will ensure him a permanent place in the history of probability.”1 This theorem is stated by Cajori in these terms: “If (r+s)nt, where the letters are integers and t=r+s, is expanded by the binomial theorem, then by taking n large enough the ratio of u (denoting the sum of the greatest term and the n preceding terms and the n following terms) to the sum of the remaining terms may be made as great as we please. Letting r and s be proportional to the probability of the happening and failing of an event in a single trial, then u corresponds to the probability that in nt trials the number of times an event happens will lie between n(r−1) and n(r+1), both inclusive.”2


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