Exact bounds of the Möbius inverse of monotone set functions

We give the exact upper and lower bounds of the Möbius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of nn elements. We find that the absolute value of the bounds tend to 4n/2πn/2 when nn is large. We establish also the exact bounds of the interaction transform and Banzhaf interaction transform, as well as the exact bounds of the Möbius inverse for the subfamilies of kk-additive normalized capacities and pp-symmetric normalized capacities.