Bijective mapping preserving intersecting antichains for -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 k -valued n -cube and the set of intersecting antichains in the k -valued ( n − 1 ) -cube.