CLOCK THEOREM AND DISTANCE FORMULA FOR STATES OF TRINITIES (Intelligence of Low-dimensional Topology)

Abstract

The purpose of this note is twofold. First, we recall a recent extension, by the author and C. Hine, of Kauffman's Clock Theorem to certain combinatorial objects called trinities. The essential part of our theorem is that the state transition graph of a trinity is always connected. Our second purpose is to announce a formula for the distance, in the state transition graph, between two arbitrary states. The proof of this formula will appear elsewhere.