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arXiv · 1112.4782

Tree modules and counting polynomials

Ryan Kinser
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Abstract

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.

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Ryan Kinser. 2012-08-25. Tree modules and counting polynomials. https://doi.org/10.1007/s10468-012-9359-x

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