Ducci Matrices in $p$-adic Context
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913721902694400 |
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| author | Giacomelli, Piero |
| author_facet | Giacomelli, Piero |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04182 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ducci Matrices in $p$-adic Context Giacomelli, Piero Number Theory Combinatorics 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. |
| title | Ducci Matrices in $p$-adic Context |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2503.04182 |