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Tree modules and counting polynomials

We give a formula for counting tree modules for the quiver S_g 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 S_g is polynomial in g with the same degree and leading coefficient as the counting polynomial A_{S_g}(d, q) for absolutely indecomposables over F_q, evaluated at q=1.

preprint2012arXivOpen access
Ryan Kinser
math.RT
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Ryan Kinser

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