In graduate school, I dreamt that God told me, "This is the fundamental unit of information." And I saw partitions (Young tableau, French notation) in which each cell was filled with either a long slash or a short slash.

Challenge: Express "the fundamental unit of information" in terms of paths down Pascal's triangle.

• Is this related to Lyndon words on two letters?
• Is this related to the forgotten basis of the symmetric functions, evaluated at the eigenvalues of a matrix?
• Is this related to {$F_2$}?