Operad of posets 101: The Wixárika 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 Wixárika 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.

19 pages, we changed the notation and content to help students follow the notes. Accepted on Special Issue on Pakistani Nobel Laureate Prof. Abdus Salam. Notes used to give a minicourse in Govt. College University Lahore in Pakistan 2022, and at the BIRS-CMO workshop "6th meeting of the Mexican Mathematicians in the World'' 2024