Tree modules and counting polynomials
Abstract
We give a formula for counting tree modules for the quiver Sg with g loops and one vertex in terms of tree modules on its universal cover. This formula, along with work of Helleloid and Rodriguez-Villegas, is used to show that the number of d-dimensional tree modules for Sg is polynomial in g with the same degree and leading coefficient as the counting polynomial ASg(d, q) for absolutely indecomposables over Fq, evaluated at q=1.
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