Discrete Euler integration over functions on finite categories

TL;DR

This paper develops a theory of Euler characteristic integration over finite categories and demonstrates its application in target enumeration on posets using sensor data, offering a discrete analogue to existing topological methods.

Contribution

It introduces a new discrete integration framework over finite categories, extending topological Euler characteristic concepts to categorical structures.

Findings

Established a formal theory of Euler integration over finite categories

Applied the theory to sensor-based target enumeration on posets

Demonstrated the discrete analogue to topological Euler characteristic-based integral theory

Abstract

This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a poset. This is a discrete analogue to Baryshnikov and Ghrist's work on integral theory using topological Euler characteristics.