2016/09/27 by Alexander Levin, Levin, Alexander
Mathematics · #12H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:12H10
paper · pdf · doi:10.48550/arxiv.1609.08544
16 pages
arxiv created 2016/09/27 · arxiv updated 2016/09/28
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.