Discrete diagonal recurrences and discrete minimal submanifolds

TL;DR

This paper explores multivariate discrete recurrences, providing solutions, structural insights, and a novel perspective on discrete minimal submanifolds, with implications for understanding complex recurrence relations.

Contribution

It introduces new solutions and structural analysis for multivariate recurrences and offers a fresh viewpoint on discrete minimal submanifolds.

Findings

Solutions for various multivariate recurrences

Structural understanding of recurrence relations

New perspective on discrete minimal submanifolds

Abstract

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic equation, and multivariate diagonal recurrences of superior order. We find the solutions, we clarify the structural background and provides short, conceptual proofs. The original results include a new point of view on discrete minimal submanifolds.