Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations
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We consider Hilbert-type functions associated with finitely generated inversive difference field extensions and systems of algebraic difference equations in the case when the translations are assigned positive integer weights. We prove that such functions are quasi-polynomials that can be represented as alternating sums of Ehrhart quasi-polynomials of rational conic polytopes. In particular, we generalize the author’s results on difference dimension polynomials and their invariants to the case of inversive difference fields with weighted basic automorphisms.
KeywordsInversive difference field Inversive difference polynomials Characteristic set Dimension quasi-polynomial
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