User blog comment:Boris Huller/Down arrow notation/@comment-35039730-20180511144816/@comment-25601061-20180511235115

Huller matrix and Hu(n) have growth rate ω22

Grand Hu(n) has growth rate ω22+1, and replacing grand with great or great with giant adds 1 to the growth rate.

However, if I understood it correctly, your extension to chained arrow notation based on your down arrow and vertical arrow system has growth rate ωω+1. Otherwise, it has growth rate ω3.