Solutions to the First Order Difference Equations in the Multivariate Difference Field
Combinatorics
2024-01-26 v1
Abstract
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference field, in which the summation problem could be transformed into solving the first order difference equations. We then show a criterion for deciding whether the difference equation has a rational solution and present an algorithm for computing one rational solution of such a difference equation, if it exists. Moreover we get the rational solution set of such an equation.
Cite
@article{arxiv.2401.13933,
title = {Solutions to the First Order Difference Equations in the Multivariate Difference Field},
author = {Lixin Du and Yarong Wei},
journal= {arXiv preprint arXiv:2401.13933},
year = {2024}
}