Bijective mapping preserving intersecting antichains for kk-valued cubes

Generalizing a result of Miyakawa, Nozaki, Pogosyan and Rosenberg, we prove that there exists a one-to-one correspondence between the set of intersecting antichains in a subset of the lower half of the kk-valued nn-cube and the set of intersecting antichains in the kk-valued (n−1)(n−1)-cube.