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CUNTZ–KRIEGER ALGEBRAS AND A GENERALIZATION OF CATALAN NUMBERS

KENGO MATSUMOTO

Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan

https://doi.org/10.1142/S0129167X13500407Cited by:2 (Source: Crossref)

Abstract

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

Keywords:

AMSC: Primary: 46L05, Secondary: 05A15

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