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Difference dimension quasi-polynomials. (English) Zbl 1418.12003

The author considers 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. He shows that such functions are quasi-polynomials, which can be represented as alternating sums of Ehrhart quasi-polynomials associated with rational conic polytopes. In particular, he obtains generalizations of main theorems on difference dimension polynomials and their invariants to the case of weighted basic difference operators.

MSC:

12H10 Difference algebra
39A05 General theory of difference equations
39A14 Partial difference equations
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References:

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