Subschemes of the Johnson scheme

Abstract Let X = ( X, {R i } i =0 d ) and X ′ = ( X′, {R′ i } i =0 d ′ ) be two association schemes defined on the same set X . We say thatX′is a subscheme ofXif each relation R′ i is a union of some R i . The subscheme lattice of the Johnson scheme J(n, m) is studied. We prove that it is trivial for m ≥ 3n + 4 ≥ 13 .