A Left Weighted Catalan Extension

Integers ◽  
2010 ◽  
Vol 10 (6) ◽  
Author(s):  
Paul R. F. Schumacher

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


Author(s):  
Muzafer Saračević ◽  
Edin Korićanin ◽  
Enver Biševac

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.





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.



2010 ◽  
Vol 53 (9) ◽  
pp. 2473-2488 ◽  
Author(s):  
ZhiWei Sun


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.



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


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