Posets with maximal Möbius function

Posets with maximal Möbius function

The absolute value of the Möbius function of a bounded poset P with n + 2 elements satisfies |μ(P )| ≤ max r≥0 max p1+...+pr=n pi≥1 r ∏

Möbius function of semigroup posets through Hilbert series

In this paper, we investigate the Möbius function μS associated to a (locally finite) poset arising from a semigroup S of Zm. We introduce and develop a new approach to study μS by using the Hilbert series of S. The latter enables us to provide formulas for μS when S belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup...

On the Möbius Function and Topology of General Pattern Posets

We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the Möbius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the Möbius ...

Fast Möbius Inversion in Semimodular Lattices and ER-labelable Posets

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e) elementary arithmetic operations, where e denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorit...

A weighted Möbius function