Difference dimension quasi-polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2017Embargo end date: 01 Jan 2016 English Publisher:Elsevier BVJournal:Advances in Applied Mathematics, volume 89, pages 1-17 (issn: 0196-8858,

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Authors: Alexander B. Levin;

doi: 10.1016/j.aam.2017.02.003 , 10.48550/arxiv.1609.08544

arXiv: 1609.08544

Difference dimension quasi-polynomials

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Abstract

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 alternative 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.

16 pages

Related Organizations

Catholic University of America
United States

Keywords

12H10, Partial difference equations, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), difference ring, difference transcendence degree, difference ideal, FOS: Mathematics, Difference algebra, General theory of difference equations, Ehrhart quasi-polynomial

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