Combinatorics around the Painleve VI

Anatol N. Kirillov
Research Institute for Mathematical Sciences (RIMS)
Kyoto University
Kyoto 606-8502
Japan

Abstract    Full Text PDF

We describe a new two-parameters family of rational solutions to the Painleve VI equation. As an application, we prove a few combinatorial identities involving Narayana's numbers and their generalizations. Also, some connections with certain special functions will be outlined.