Operad of posets 101: The Wix\'arika posets

TL;DR

This paper introduces Wixárika posets as a suboperad of the operad of posets, providing a new algebraic framework to analyze their combinatorial structure.

Contribution

It presents a novel example of a suboperad of posets, illustrating key structural features and deepening the understanding of their operadic relationships.

Findings

Wixárika posets form a rich suboperad with distinctive structural properties.

The operad framework clarifies the combinatorial relationships of these posets.

The example balances complexity and accessibility, aiding further research.

Abstract

We study classes of objects whose combinatorics are closely related to those of posets. The framework of operads and operad algebras allows us to make this relationship precise and provides tools for a deeper understanding of their combinatorial structure. In this note, we present a nontrivial example of a suboperad of the operad of posets, called Wix\'arika posets, together with its associated algebras. This example is sufficiently rich to exhibit key structural features of the theory, while remaining accessible and avoiding unnecessary technicalities.