Unimodular Valuations beyond Ehrhart
Ansgar Freyer, Monika Ludwig, Martin Rubey
TL;DR
This paper classifies unimodular valuations on lattice polygons, extending previous work by analyzing their behavior under dilation and using invariant theory to provide a comprehensive framework.
Contribution
It provides a complete classification of unimodular valuations on lattice polygons beyond Ehrhart, utilizing dilation behavior and invariant theory.
Findings
Classified unimodular valuations on lattice polygons.
Extended valuations to unbounded polyhedra.
Connected valuations with invariant theory.
Abstract
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with respect to dilation using extensions to unbounded polyhedra and basic invariant theory.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models