Explicit semisymmetric chain decomposition of the partition lattice

Loeb et al. (J. Combin. Theory. Ser A. 65 (1994) 151–157) gave an explicit semisymmetric chain decomposition of Π(n). In this paper we give a second explicit semisymmetric chain decomposition and show that it is different from the one given in Loeb et al. (1995) in the sense that no order automorphism of Π(n) can carry one to another.