A theory of pictures for quasi-posets

TL;DR

This paper extends the theory of pictures from posets to quasi-posets, connecting combinatorics of symmetric groups with topology, and exploring their applications in Young diagrams and tableaux.

Contribution

It introduces a generalized framework for pictures between quasi-posets, broadening the combinatorial and topological understanding of these structures.

Findings

Extended the theory of pictures to quasi-posets

Linked quasi-posets with finite topologies

Provided new insights into Young diagrams and tableaux

Abstract

The theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as Young diagrams and tableaux. Many reasons, com-binatorial (e.g. since semi-standard tableaux can be viewed as double quasi-posets) and topological (quasi-posets identify with finite topolo-gies) lead to extend the theory to quasi-posets. This is the object of the present article.