Cuntz-krieger Algebras and a Generalization of Catalan Numbers
نویسنده
چکیده
We first observe that the relations of the canonical generating isometries of the Cuntz algebra ON are naturally related to the N-colored Catalan numbers. For a directed graph G, we generalize the Catalan numbers by using the canonical generating partial isometries of the Cuntz-Krieger algebra O AG for the transition matrix A of G. The generalized Catalan numbers cGn , n = 0, 1, 2, . . . enumerate the number of Dyck paths and oriented rooted trees for the graph G. Its generating functions will be studied.
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