Finite Codes and Groupoid Words

Correspondences between codes and groupoid words are established: between maximal suffix codes and groupoid words; between maximal commutatively prefix codes and cancellative entropic groupoid words; and between finite maximal codes and idempotent entropic groupoid words. Recognition criteria for the three types of groupoid word are given in terms of order relations involving binomial coefficients, divisibility conditions, partition functions and curves in simplices