A Discrete Bochner–Martinelli Formula

A discrete Lefschetz formula

A Lefschetz formula is given that relates loops in a regular finite graph to traces of a certain representation. As an application the poles of the Ihara/Bass zeta function are expressed as dimensions of global section spaces of locally constant sheaves.

A discrete Faà di Bruno's formula

We derive a discrete Faà di Bruno’s formula that rules the behaviour of finite differences under composition of functions with vector values and arguments.

A proof of Ito ' s formula using a discrete Ito ' s formula

A Haar wavelets approach to Stirling's formula

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

An Abramov Formula for Stationary Spaces of Discrete Groups

Let (G,μ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A μ-random walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the random walk first hits Γ. We prove that the Furstenberg entropy of a (G,μ)-stationary space, with respect to the...