Cuntz-Krieger algebras and a generalization of Catalan numbers

Simple item page
dc.creatorMatsumoto, Kengo
dc.date2006-07-21
dc.date2006-08-18
dc.date.accessioned2026-07-07T07:20:45Z
dc.date.available2026-07-07T07:20:45Z
dc.descriptionWe first observe that the relations of the canonical generating isometries of the Cuntz algebra ${\cal O}_N$ 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 ${\cal O}_{A^G}$ for the transition matrix $A^G$ of $G$. The generalized Catalan numbers $c_n^G, n=0,1,2,...$ enumerate the number of Dyck paths and oriented rooted trees for the graph $G$. Its generating functions will be studied.
dc.description24pages, 5figures
dc.identifierhttps://arxiv.org/abs/math/0607517
dc.identifierhttp://arxiv.org/abs/math/0607517
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115063
dc.subjectOperator Algebras
dc.subjectCombinatorics
dc.subject05A15;46L05
dc.titleCuntz-Krieger algebras and a generalization of Catalan numbers
dc.typetext

Files

Collections

arXiv