The Shortest Interesting Binary Words

I will show that there exist two binary words (one of length 4 and one of length 6) that play a special role in many different problems in combinatorics on words. They can therefore be considered $\mathit{\text{the}}\mathit{\text{shortest}}\mathit{\text{interesting}}\mathit{\text{binary}}\mathit{\text{words}}$. My claim is supported by the fact that these two words appear in dozens of papers in combinatorics on words.