Given the famous Littlewood-Richardson rule, in terms of Schur polynomials:


$$s\_\mu s\_\nu=\sum\_\lambda c^{\lambda}\_{\mu\nu} s\_\lambda,$$


is there a classification of the cases where the LR coefficients are equal to 1?



When the Littlewood-Richardson rule gives only irreducibles?
The answer is **Yes**, but this requires some elaboration.


1. [Knutson-Tao-Woodward](https://arxiv.org/abs/math/0107011) prove Fulton's conjecture in $\S$6.1. In principle, you can follow the approach by [De Loera-McAllister](https://arxiv.org/abs/math/0501446) or [Mulmuley-Narayanan-Sohoni](https://www.emis.de/journals/JACO/Volume36_1/rg1w9655642r84t8.fulltext.pdf), to convert the result into a statement about certain polytopes being single points.
2. [Bürgisser-Ikenmeyer](https://arxiv.org/abs/1204.2484) make the answer much more explicit, see Prop. 3.13. Ikenmeyer further generalized this in to $c^\lambda\_{\mu\nu}>t$ in [his thesis](https://www3.math.tu-berlin.de/algebra/work/ikenmeyer_thesis.pdf), see Theorem 11.3.2.


