Posets That Locally Resemble Distributive Lattices An Extension of Stanley's Theorem (with Connections to Buildings and Diagram Geometries)

AbstractLet P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed

Semi-primary lattices and tableau algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.Includes bibliographical references (leaves 194-195).by Glenn Paul Tesler.Ph.D