Interacting columns: generating functions and scaling exponents

A model of self-interacting columns, related to modi:ls of partially direct ed walks and to histogram polygons, is considered. The generating function of this model is found in terms of q-deformed Bessel functions using a func tional recursion scheme. A transition, related to a deflation-inflation tra nsition seen in staircase polygons, or to a rc,ugh-smooth transition in a s olid-on-solid model, is found, and its scaling exponents are found in the c ontext of a tricritical scaling analysis. If the columns are also interacti ng with the horizontal axis, then the inflated or smooth phase is also foun d to undergo an adsorption transition. A special point exists where the mod el is critical with respect to both an adsorption transition and a deflatio n-inflation transition.