A Dynkin diagram classification theorem arising from a combinatorial problem

Birkhoff, 1967 Cańfield, 1980, A Sperner property preserved by products, Linear and Multilinear Algebra, 9, 151, 10.1080/03081088008817361 Greene, 1978, Proof techniques in the theory of finite sets Griggs, 1980, On chains and Sperner k-Families in ranked posets, II, J. Combin. Theory Ser. A, 29, 391, 10.1016/0097-3165(80)90039-4 Harper, 1984, Morphisms for the strong Sperner property of Stanley and Griggs, Linear and Multilinear Algebra, 16, 323, 10.1080/03081088408817635 Hazewinkel, 1977, The ubiquity of Coxeter-Dynkin diagrams, Nieuw Arch. Wisk., 25, 257 Humphreys, 1970 Proctor, 1982, Representations of sl(2, C) on posets and the Sperner property, SIAM J. Algebraic Discrete Methods, 3, 275, 10.1137/0603026 Proctor, 1984, Bruhat latices, plane partition generation generating functions, and minuscule representations, European J. Combin., 5, 331, 10.1016/S0195-6698(84)80037-2 Proctor, 1982, Solution of two difficult combinatorial problems with linear algebra, Amer. Math. Monthly, 89, 721, 10.2307/2975833 Proctor, 1980, Product partial orders with the Sperner property, Discrete Math., 30, 173, 10.1016/0012-365X(80)90118-1 Stanley, 1980, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Algebraic Discrete Methods, 1, 168, 10.1137/0601021 Stanley, 1984, Quotients of Peck posets, Order, 1, 29, 10.1007/BF00396271 Wolf, 1967