Difference dimension quasi-polynomials

We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that such functions are quasi-polynomials, which can be represent...

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Bibliographic Details
Published in:Advances in applied mathematics 2017-08, Vol.89, p.1-17
Main Author: Levin, Alexander
Format: Article
Language:English
Subjects:
Difference ideal
Difference ring
Difference transcendence degree
Ehrhart quasi-polynomial
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Summary:We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that such functions are quasi-polynomials, which can be represented as alternating sums of Ehrhart quasi-polynomials associated with rational conic polytopes. In particular, we obtain generalizations of main theorems on difference dimension polynomials and their invariants to the case of weighted basic difference operators.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2017.02.003