Incidence algebra

Summary

The incidence algebra of a locally finite partially ordered set is the algebra of functions on its intervals, multiplied by a convolution. Its most important elements are the zeta function, which is $1$ on every interval, and its inverse, the Möbius function of the poset. It gives a common setting for inclusion–exclusion, the number-theoretic Möbius inversion formula and the calculus of finite differences, through Möbius inversion on posets.