منابع مشابه
Envelopes of Geometric Lattices
A categorical embedding theorem is proved for geometric lattices. This states roughly that, if one wants to consider only those embeddings into pro-jective spaces having a suitable universal property, then the existence of such an embedding can be checked by seeing whether corresponding properties hold for many small intervals. Tutte's embedding theorem for binary geometric lattices is a conseq...
متن کاملFinite distributive lattices are congruence lattices of almost- geometric lattices
A semimodular lattice L of finite length will be called an almost-geometric lattice, if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.
متن کاملBasis-homogeneous Geometric Lattices
We classify the finite point—and basis—homogeneous geometric lattices having a line of size greater than 2. As a consequence, the finite basis-homogeneous geometric lattices are known, up to the knowledge of those having only lines of size 2.
متن کاملGeometric Lattices of Structured Partitions
*Research and preparation of this report were substantially assisted by National Science Foundation grants DMS-8407102 and DMS-8606102. For certain matroids on the edges of a graph, digraph, or bidirected graph with group gains (edge labels from a group), the ats form intriguing new geometric lattices whose Whitney numbers have geometrical signiicance. In this chapter, the rst of a series, we l...
متن کاملModular Elements of Geometric Lattices
Let L be a finite geometric lattice of rank n with rank function r. (For definitions, see e.g., [3, Chapter 2], [4], or [1, Chapter 4].) An element x s L is called a modular element if it forms a modular pair with every y e L , i.e., if a<~y then a V ( x A y ) = (a v x )Ay . Recall that in an upper semimodular lattice (and thus in a geometric lattice) the relation of being a modular pair is sym...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1975
ISSN: 0097-3165
DOI: 10.1016/0097-3165(75)90062-x