order; product of chains; ideal of maximum height; digit sum sequence
We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.
 Davey, B. A., Priestley, H. A.: Introduction to Lattices and Order
. Second edition, Cambridge University Press, New York (2002), xii+298. MR 1902334
| Zbl 1002.06001
 Grätzer, G.: General Lattice Theory
. New appendices with B. A. Davey, R. Freese, B. Ganter, M. Greferath, P. Jipsen, H. A. Priestley, H. Rose, E. T. Schmidt, S. E. Schmidt, F. Wehrung, R. Wille; Second edition. Birkhäuser, Basel (1998). MR 1670580