  Aim of this paper is to count $0$-dimensional stable and strongly stable
ideals in $2$ and $3$ variables, given their (constant) affine Hilbert
polynomial.
  To do so, we define the Bar Code, a bidimensional structure representing any
finite set of terms $M$ and allowing to desume many properties of the
corresponding monomial ideal $I$, if $M$ is an order ideal. Then, we use it to
give a connection between (strongly) stable monomial ideals and integer
partitions, thus allowing to count them via known determinantal formulas.
