scholarly journals Congruences related to dual sequences and Catalan numbers

2022 ◽  
Vol 101 ◽  
pp. 103458
Author(s):  
Rong-Hua Wang ◽  
Michael X.X. Zhong
Keyword(s):  
Catalan Numbers ◽  
Dual Sequences

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 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.

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