We investigate tile poset S
π
(G)/G of conjugacy clases of subgroups of π-power index in a finite group G. In particular, we are concerned with combinatorial and topological properties of the order ...complex of S
π
(G)/G. We show that the order complex of S
π
(G)/G iS homotopic to a join of orbit spaces of order complexes of posets, which bear structural information on the cheif factors of the group. Moreover, for π-solvable groups and in case π = {p} we reveal a shellable subposer of S
π
(G)/G of the same homotopy type. This complements the study of the poset S
π
(G) of subgroups of π-power index performed in 20. For the analysis of the order complexes we develop some new lemmata on the topology of order complexes of posets and in the theory of shellability.
Orthogonal forms of positive Boolean functions play an important role in reliability theory, since the probability that they take value 1 can be easily computed. However, few classes of disjunctive ...normal forms are known for which orthogonalization can be efficiently performed. An interesting class with this property is the class of shellable disjunctive normal forms (DNFs). In this paper, we present some new results about shellability. We establish that every positive Boolean function can be represented by a shellable DNF, we propose a polynomial procedure to compute the dual of a shellable DNF, and we prove that testing the so-called lexico-exchange (LE) property (a strengthening of shellability) is NP-complete.
The class ofStrongly Signablepartially ordered sets is introduced and studied. It is show that strong signability, reminiscent of Björner–Wachs' recursive coatom orderability, provides a useful and ...broad sufficient condition for a poset to be dual CR and hence partitionable. The flagh-vectors of strongly signable posets are therefore non-negative. It is proved that recursively shellable posets, polyhedral fans, and face lattices of partitionable simplicial complexes are all strongly signable, and it is conjectured that all spherical posets are. It is concluded that the barycentric subdivision of a partitionable complex is again partitionable, and an algorithm for producing a partitioning of the subdivision from a partitioning of the complex is described. An expression for the flagh-polynomial of a simplicial complex in terms of itsh-vector is given, and is used to demonstrate that the flagh-vector is symmetric or non-negative whenever theh-vector is.
Provider: - Institution: - Data provided by Europeana Collections- Bremen, Universität Bremen, Diss., 2014- All metadata published by Europeana are available free of restriction under the Creative ...Commons CC0 1.0 Universal Public Domain Dedication. However, Europeana requests that you actively acknowledge and give attribution to all metadata sources including Europeana
PDF
