Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4653552 | European Journal of Combinatorics | 2014 | 28 Pages |
Abstract
For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e. This construction, which contains the poset Clop(e) of all clopen sets, is a common generalization of known notions such as the generalized permutohedron on a partially ordered set on the one hand, and the bipartition lattice on a set on the other hand. We obtain a precise description of the completely join-irreducible (resp., meet-irreducible) elements of Reg(e) and the arrow relations between them. In particular, we prove that
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Luigi Santocanale, Friedrich Wehrung,