Analysis of random point images with the use of symbolic computation codes and generalized Catalan numbers

2016 ◽  
Vol 52 (6) ◽  
pp. 529-536
Author(s):  
A. L. Reznik ◽  
A. V. Tuzikov ◽  
A. A. Solov’ev ◽  
A. V. Torgov
Keyword(s):  
Symbolic Computation ◽  
Catalan Numbers ◽  
Random Point ◽  
Generalized Catalan Numbers ◽  
Computation Codes

Generalized Catalan numbers in problems of processing of random discrete images

2011 ◽  
Vol 47 (6) ◽  
pp. 533-536
Author(s):  
A. L. Reznik ◽  
V. M. Efimov ◽  
A. A. Solov’ev ◽  
A. V. Torgov
Keyword(s):  
Catalan Numbers ◽  
Generalized Catalan Numbers

scholarly journals Bijections between noncrossing and nonnesting partitions for classical reflection groups

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Alex Fink ◽  
Benjamin Iriarte Giraldo
Keyword(s):  
Type A ◽  
Reflection Group ◽  
Catalan Numbers ◽  
Reflection Groups ◽  
Generalized Catalan Numbers ◽  
Elementary Methods ◽  
International Audience ◽  
Type Sets

International audience We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in the literature. To find them we define, for every type, sets of statistics that are in bijection with noncrossing and nonnesting partitions, and this correspondence is established by means of elementary methods in all cases. The statistics can be then seen to be counted by the generalized Catalan numbers Cat$(W)$ when $W$ is a classical reflection group. In particular, the statistics of type $A$ appear as a new explicit example of objects that are counted by the classical Catalan numbers.

scholarly journals On Teaching of Generalized Catalan Numbers with the Maple´s Help

2018 ◽  
Vol 11 (1) ◽  
pp. 25-40
Author(s):  
Francisco Regis Vieira Alves ◽  
Keyword(s):  
Catalan Numbers ◽  
Generalized Catalan Numbers

scholarly journals CUNTZ–KRIEGER ALGEBRAS AND A GENERALIZATION OF CATALAN NUMBERS

2013 ◽  
Vol 24 (05) ◽  
pp. 1350040 ◽  
Author(s):  
KENGO MATSUMOTO
Keyword(s):  
Directed Graph ◽  
Generating Functions ◽  
Transition Matrix ◽  
Catalan Numbers ◽  
Partial Isometries ◽  
Dyck Paths ◽  
Generalized Catalan Numbers

For a directed graph G, we generalize the Catalan numbers by using the canonical generating partial isometries of the Cuntz–Krieger algebra [Formula: see text] for the transition matrix AGof the directed edges of G. The generalized Catalan numbers [Formula: see text] enumerate the number of Dyck paths for the graph G. Its generating functions will be studied.

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