Numerical semigroups in a problem about economic incentives for consumers

TL;DR

This paper introduces the concept of C-incentives in the context of economic incentives for consumers, providing algorithms to compute and analyze these structures using numerical semigroup theory.

Contribution

It defines C-incentives, proves their structure as a Frobenius pseudo-variety, and develops algorithms for their computation and construction.

Findings

The set of all numerical C-incentives forms a Frobenius pseudo-variety.

Algorithms are provided to compute the smallest C-incentive containing a given set.

A recursive process to build the pseudo-variety of numerical C-incentives is established.

Abstract

Motivated by a promotion to increase the number of musical downloads, we introduce the concept of $C$-incentive and show an algorithm that compute the smallest $C$-incentive containing a subset $X \subseteq {\mathbb N}$. On the other hand, in order to study $C$-incentives, we see that we can focus on numerical $C$-incentives. Then, we establish that the set formed by all numerical $C$-incentives is a Frobenius pseudo-variety and we show an algorithmic process to recurrently build such a pseudo-variety.