A Left Weighted Catalan Extension

Integers ◽  
2010 ◽  
Vol 10 (6) ◽  
Author(s):  
Paul R. F. Schumacher
Keyword(s):  
Catalan Numbers ◽  
Ballot Problem

AbstractThere are many representations of the Catalan numbers. In this article, we will examine the ballot problem and extend it beyond the standard

scholarly journals Encryption based on Ballot, Stack permutations and Balanced Parentheses using Catalan-keys

2018 ◽  
Vol 14 (2) ◽  
Author(s):  
Muzafer Saračević ◽  
Edin Korićanin ◽  
Enver Biševac
Keyword(s):  
Combinatorial Problems ◽  
Catalan Numbers ◽  
Java Application ◽  
Encryption And Decryption ◽  
Ballot Problem

This paper examines the possibilities of applying Catalan numbers in cryptography. It also offers the application of appropriate combinatorial problems (Ballot Problem, Stack permutations and Balanced Parentheses) in encryption and decryption of files and plaintext. The paper analyzes the properties of Catalan numbers and their relation to these combined problems. Applied copyright method is related to the decomposition of Catalan numbers in the process of efficient keys generating. Java software solution which enables key generating with the properties of the Catalan numbers is presented at the end of the paper. Java application allows encryption and decryption of plaintext based on the generated key and combinatorial problems.

Families of linear recurrences for Catalan numbers

2011 ◽  
Vol 42 (1) ◽  
pp. 131-139 ◽  
Author(s):  
N. Gauthier
Keyword(s):  
Catalan Numbers ◽  
Linear Recurrences

scholarly journals ON DIVISIBILITY OF BINOMIAL COEFFICIENTS

2012 ◽  
Vol 93 (1-2) ◽  
pp. 189-201 ◽  
Author(s):  
ZHI-WEI SUN
Keyword(s):  
Higher Order ◽  
Catalan Numbers ◽  
Binomial Coefficients

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

scholarly journals Binomial coefficients, Catalan numbers and Lucas quotients

2010 ◽  
Vol 53 (9) ◽  
pp. 2473-2488 ◽  
Author(s):  
ZhiWei Sun
Keyword(s):  
Catalan Numbers ◽  
Binomial Coefficients

scholarly journals Associative spectra of graph algebras I

2021 ◽  
Author(s):  
Erkko Lehtonen ◽  
Tamás Waldhauser
Keyword(s):  
Catalan Numbers ◽  
Graph Algebras ◽  
Undirected Graphs ◽  
Powers Of 2

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.

New Expressions for Sums of Products of the Catalan Numbers

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 330
Author(s):  
Conghui Xie ◽  
Yuan He
Keyword(s):  
Arbitrary Number ◽  
Catalan Numbers ◽  
Bell Polynomials ◽  
Sums Of Products

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.

scholarly journals Several series identities involving the Catalan numbers

2018 ◽  
Vol 172 (3) ◽  
pp. 466-474 ◽  
Author(s):  
Li Yin ◽  
Feng Qi
Keyword(s):  
Catalan Numbers
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