The Möbius function and distal flows

The Möbius Function and Distal Flows

We prove that the Möbius function is linearly disjoint from an analytic skew product on the 2-torus. These flows are distal and can be irregular in that their ergodic averages need not exist for all points. We also establish the linear disjointness of Möbius from various distal homogeneous flows.

The Möbius Function of Separable and Decomposable

We give a recursive formula for the Möbius function of an interval [σ, π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1, 2, . . . , k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficie...

A weighted Möbius function

Computing the Summation of the 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 ∏