Séminaire Lotharingien de Combinatoire, B54f (2006), 17 pp.

Yvan Le Borgne

Counting Upper Interactions in Dyck Paths

Abstract. Upper and lower interactions are parameters of Dyck paths which are motivated by corresponding parameters in a model of partially directed polymers. We investigate the problem of obtaining the generating function for Dyck paths with respect to upper interactions in terms of basic hypergeometric q-series in which an algebraic term occurs.

Received: August 8, 2005. Revised: October 10, 2005. Accepted: December 20, 2005. Final Version: February 8, 2006.

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