Möbius function on cross-section lattices

Lattices, Möbius Functions and Communication Complexity

In a recent paper, Hajnal, Maass and Tura'n analyzed the communication complexity of graph connectivity. Building on this work, we develop a general framework for the study of a broad class of communication problems which has several interesting special cases including the graph connectivity problem. The approach is based on combinatorial lattice theory.

A weighted 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 ∏

Counting Restricted Homomorphisms via Möbius Inversion over Matroid Lattices

We present a framework for the complexity classification of parameterized counting problems that can be formulated as the summation over the numbers of homomorphisms from small pattern graphs H1, . . . ,H` to a big host graph G with the restriction that the coefficients correspond to evaluations of the Möbius function over the lattice of a graphic matroid. This generalizes the idea of Curticape...

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...