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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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