Difference dimension quasi-polynomials

作者：Levin Alexander^*

来源：Advances in Applied Mathematics, 2017, 89: 1-17.

DOI：10.1016/j.aam.2017.02.003

• Difference ring
• Difference ideal
• Ehrhart quasi-polynomial
• Difference transcendence degree

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.

• 出版日期2017-8