Every finite lattice can be embedded in a finite partition lattice
Pavel Pudi · 1980
We give here a proof of theorem stated in title. The theorem was conjectured by P. M. Whitman in [11]. The proof, mostly of combinatorial character, is based on the regraph power technique making use of special edge-colored graphs, called regraphs, as construction schemes. We use proof of Combinatorial Lemma 6.1 by B. Wolk and B. Sands, which is shorter and more elegant than original one. The list of references is a random collection of papers related to Whitman's conjecture. 1. The class of finite lattices Here we present a simple method of generating all lattices. We shall use notion of join-homomorphis m, meet-homomorphis m, order preserving mapping and lattice embedding in sense of [2]. The greatest and least elements of a lattice L will be denoted by 1L, Or_.