# Product of two staircase rank one transformations that is not loosely Bernoulli

## TL;DR

This paper constructs two specific staircase rank one transformations whose Cartesian product does not exhibit the loosely Bernoulli property, challenging assumptions about their typical behavior.

## Contribution

The paper introduces a novel example of staircase rank one transformations with a non-loosely Bernoulli product, providing new insights into their dynamical properties.

## Key findings

- Constructed two staircase rank one transformations
- Their Cartesian product is not loosely Bernoulli
- Challenges previous assumptions about typical behavior

## Abstract

We construct two staircase rank one transformations whose Cartesian product is not loosely Bernoulli.