Pascal' Triangle and Catalan Numbers

Author(s):  
Thomas Koshy
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


2012 ◽  
Vol 93 (1-2) ◽  
pp. 189-201 ◽  
Author(s):  
ZHI-WEI SUN

AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.


Author(s):  
Erkko Lehtonen ◽  
Tamás Waldhauser

AbstractAssociative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.


Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 330
Author(s):  
Conghui Xie ◽  
Yuan He

In this paper, we perform a further investigation for the Catalan numbers. By making use of the method of derivatives and some properties of the Bell polynomials, we establish two new expressions for sums of products of arbitrary number of the Catalan numbers. The results presented here can be regarded as the development of some known formulas.


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