scholarly journals A Note on Super Catalan Numbers

2012 ◽  
Vol 18 (1) ◽  
pp. 23-24
Author(s):  
Evangelos GEORGIADIS ◽  
Akihiro MUNEMASA ◽  
Hajime TANAKA
Keyword(s):  
Catalan Numbers ◽  
Super Catalan Numbers

scholarly journals Remarks on Catalan and super-Catalan numbers

2011 ◽  
Vol 96 ◽  
pp. 237-244
Author(s):  
Anna Dorota Krystek ◽  
Łukasz Jan Wojakowski
Keyword(s):  
Catalan Numbers ◽  
Super Catalan Numbers

scholarly journals Matchings Avoiding Partial Patterns

10.37236/1138 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
William Y. C. Chen ◽  
Toufik Mansour ◽  
Sherry H. F. Yan
Keyword(s):  
Catalan Numbers ◽  
Schröder Numbers ◽  
Schröder Paths ◽  
Generating Trees ◽  
Super Catalan Numbers ◽  
Wilf Equivalence

We show that matchings avoiding a certain partial pattern are counted by the $3$-Catalan numbers. We give a characterization of $12312$-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns $12312$ and $121323$ and Schröder paths without peaks at level one, which are counted by the super-Catalan numbers or the little Schröder numbers. A refinement of the super-Catalan numbers is derived by fixing the number of crossings in the matchings. In the sense of Wilf-equivalence, we use the method of generating trees to show that the patterns 12132, 12123, 12321, 12231, 12213 are all equivalent to the pattern $12312$.

scholarly journals Congruences on Sums of Super Catalan Numbers

2018 ◽  
Vol 73 (4) ◽  
Author(s):  
Ji-Cai Liu
Keyword(s):  
Catalan Numbers ◽  
Super Catalan Numbers

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.

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