  We give a brief account of a construction called tokens here, which is
significant in algebra, analysis, combinatorics, and physics. Tokens allow to
express a semigroup on one set via a semigroup convolution on another set.
Therefore tokens are similar to intertwining operators but are more flexible.
  Keywords: semigroups, hypergroups, tokens, poset, multiplicative functions,
polynomial sequence of binomial type, integral kernel, wavelets, refinement
equation, special functions, quantum propagator, path integral, quantum
computing.
