
TL;DR
This paper derives a generating function for the index of lattice points relative to finite order ideals, providing a new tool for border bases and solving related difference equations explicitly.
Contribution
It introduces a generating function for the index in border bases, offering a novel explicit solution to certain difference equations.
Findings
Derived the generating function for lattice point indices
Provided explicit solutions to a class of difference equations
Enhanced understanding of border bases and their computational aspects
Abstract
We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve a class of difference equations where the right-hand side is the minimum of a number of affine forms.
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Taxonomy
TopicsAgriculture and Rural Development Research
