I will give a criterion which allows to determine, in terms of the combinatorics of the root system A_n, which p-kernels occur in a given isogeny class of p-divisible groups over an algebraically closed field of positive characteristic. This question is related to the relationship between Newton and Ekedahl-Oort strata on reductions of Shimura varieties as well as the non-emptiness of affine Deligne-Lusztig varieties.