Operad of posets 101: The Wix\'arika posets

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.