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arXiv · 2503.04182

Ducci Matrices in $p$-adic Context

Piero Giacomelli
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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.

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Piero Giacomelli. 2025-03-06. Ducci Matrices in $p$-adic Context. https://arxiv.org/abs/2503.04182

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