TL;DR
This paper investigates the structure of self-joinings in 3-interval exchange transformations, revealing that most are not 2-simple and their self-joinings form a Paulsen simplex, answering a question posed by Veech.
Contribution
It demonstrates that typical 3-IETs are not 2-simple and characterizes their self-joinings as forming a Paulsen simplex, providing new insights into their dynamical properties.
Findings
Most 3-IETs are not 2-simple
Self-joinings of almost all 3-IETs form a Paulsen simplex
Addresses a question of Veech regarding 3-IETs
Abstract
We show that typical interval exchange transformations on three intervals are not 2-simple answering a question of Veech. Moreover, the set of self-joinings of almost every 3-IET is a Paulsen simplex.
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