A broad class of shellable lattices

A broad class of shellable lattices

We introduce a new class of lattices, the modernistic lattices, and their duals, the comodernistic lattices. We show that every modernistic or comodernistic lattice has shellable order complex. We go on to exhibit a large number of examples of (co)modernistic lattices. We show comodernism for two main families of lattices that were not previously known to be shellable: the order congruence latt...

Planar Lattices are Lexicographically Shellable

The special properties of planar posets have been studied, particularly in the 1970's by I. Rival and others. More recently, the connection between posets, their corresponding polynomial rings and corresponding simplicial complexes has been studied by R. Stanley and others. This paper, using work of A. Bjorner, provides a connection between the two bodies of work, by characterizing when planar...

A Class of Geometric Lattices

and that the same holds if any n— 1 of the signs are replaced by strict inequality. Those unimodular lattices, such as Z , which have only the origin in common with the open cube shall be called critical, as shall the corresponding matrices. Minkowski conjectured, and Hajos [ l ] proved in 1938, that a critical lattice must contain one of the points (5»i, • • • , 5,-»), i = 1, • • • , n. If A i...

Criterions for Shellable Multicomplexes

After [4] the shellability of multicomplexes Γ is given in terms of some special faces of Γ called facets. Here we give a criterion for the shellability in terms of maximal facets. Multigraded pretty clean filtration is the algebraic counterpart of a shellable multicomplex. We give also a criterion for the existence of a multigraded pretty clean filtration.

The Complement of a D-Tree is Pure Shellable