Publications in Scientific Journals:
J. Blieberger, P. Kirschenhofer:
"Generalized Catalan Sequences Originating from the Analysis of Special Data Structures";
Bulletin of the Institute of Combinatorics and its Applications,
71
(2014),
103
- 116.
English abstract:
Reinterpreting known results on Carlitz's q-Catalan numbers $c_n(q)$ we find a connection between the number of acyclic DJ graphs and these q-analogs. A similar recurrence relation is setup for the number of reducible DJ graphs, a well-known data structure in computer science, this time leading to a different q-analog $C_n(q)$ of Catalan numbers. Using arguments from enumerative combinatorics we establish a complete asymptotic expansion of the numbers $C_n(q)$.