Quivers and LR-coefficients

I will discuss the rich combinatorics of dimension vectors of quivers. As an application, I will describe Littlewood-Richardson coefficients which are equal to 1. The triples of partitions for which the LR-coefficient is equal to 1 can be constructed in a similar recursive way as in Horn's conjecture for eigenvalues of sums of Hermitian matrices. (Joint work with Jerzy Weyman.)