  In this short note, we draw attention to a relation between two Horn
polytopes which is proved in [Chenciner-Jim\'enez P\'erez] as the result on the
one side of a deep combinatorial result in [Fomin,Fulton, Li,Poon], on the
other side of a simple computation involving complex structures. This suggested
an inequality between Littlewood-Richardson coefficients which we prove using
the symmetric characterization of these coefficients given in
[Carr\'e,Leclerc].
