Toric arrangement and discrete truncated power

TL;DR

This paper introduces a novel approach using toric arrangements and Laplace transforms to analyze discrete truncated power, demonstrating it as a periodic piecewise polynomial on shifted lattice cones and providing a computational method.

Contribution

It presents a new toric arrangement method for computing discrete truncated power, linking it to periodic piecewise polynomial behavior.

Findings

Discrete truncated power is a periodic piecewise polynomial.

A toric arrangement method for computation is developed.

The approach uses Laplace transform and toric arrangement theory.

Abstract

In this paper, by using the Laplace transform and the theory of toric arrangement, we show that discrete truncated power is a periodic piecewise polynomial on the shifted integral lattice cone. Based on the toric reduction method in the real field, we give a toric arrangement method to compute discrete truncated power.