Cuntz-Krieger algebras and a generalization of Catalan numbers (Q2854051)
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scientific article; zbMATH DE number 6216006
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cuntz-Krieger algebras and a generalization of Catalan numbers |
scientific article; zbMATH DE number 6216006 |
Statements
17 October 2013
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Cuntz-Krieger algebras
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Catalan numbers
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Dyck paths
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directed graphs
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generating functions
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\(C^{\ast}\)-algebras
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Cuntz-Krieger algebras and a generalization of Catalan numbers (English)
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A Dyck path is a finite path of rising and falling edges and ending at the same horizontal level as started. The Catalan number is the number of such paths.NEWLINENEWLINEThe author considers similar paths in the word set of Cuntz-Krieger algebras, associated to a finite \(0,1\)-matrix \(A\), and associates generalized Catalan numbers to them.NEWLINENEWLINEUsing generating functions, an idea in combinatorics, and the Cauchy integral formula in several variables in \(\mathbb{C}\), an analytical integral formula for generalized Catalan numbers is stated.NEWLINENEWLINEThis is used to discuss several examples of graphs and compute their generalized Catalan numbers.
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