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Abstract
Following a theorem of Hayes, we give a geometric interpretation of the special value at [Formula: see text] of certain [Formula: see text]-cocycle on [Formula: see text] previously introduced by the author. This work yields three main results: an explicit formula for our cocycle at [Formula: see text], a generalization and a new proof of Hayes’ theorem, and an elegant summation formula for the zeroth coefficient of the Ehrhart quasi-polynomial of certain triangles in [Formula: see text].
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