Ducci Matrices in $p$-adic Context

Abstract

In this paper, we mutuate the concept of Ducci matrices to the $p$-adic setting, generalizing the classical Ducci sequences to the framework of $p$-adic numbers. The classical Ducci operator, which iteratively computes the absolute differences of neighboring elements in a sequence or matrix, is redefined using the $p$-adic absolute value $|\cdot {|}_p$. We investigate the dynamics of $p$-adic Ducci sequences for matrices over ${\mathbb{Q}}_p$, focusing on their convergence and periodicity properties.

10 pages