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arXiv · 2603.18065

An Algebraic Structure for the Central Mexican Ritual Calendar

Ramiro Carrillo-Catalán
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Abstract

This article develops an algebraic model of the 260-day Central Mexican ritual calendar, the \textit{Tonalpohualli}. We represent the calendar as the cyclic group $\mathbb{Z}_{13}\oplus\mathbb{Z}_{20}$, where each day name is encoded by a numeral-sign pair. From this model, we derive explicit correspondences between day numbers and day names through group actions. We also characterize, in algebraic terms, the twenty 13-day periods, the thirteen 20-day periods, and the partition of days into oriented tetrads. In addition, we describe how these structures relate to a subgroup generated by permutations of the starts of 13-day periods, and we show its connection with a cyclic group of order four and with square rotations. These results formalize and extend previous arithmetic and structural interpretations of the \textit{Tonalpohualli}, and they provide a framework for codex analysis.

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Ramiro Carrillo-Catalán. 2026-03-18. An Algebraic Structure for the Central Mexican Ritual Calendar. https://arxiv.org/abs/2603.18065

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