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A New Algorithm for Computing the Frobenius Number

Abbas Taheri, Saeid Alikhani

TL;DR

A new algorithm to calculate the Frobenius number is presented and the sequential form of the new algorithm is presented.

Abstract

A number $α$ has a representation with respect to the numbers $α_1,...,α_n$, if there exist the non-negative integers $λ_1,... ,λ_n$ such that $α=λ_1α_1+...+λ_n α_n$. The largest natural number that does not have a representation with respect to the numbers $α_1,...,α_n$ is called the Frobenius number and is denoted by the symbol $g(α_1,...,α_n)$. In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm.

A New Algorithm for Computing the Frobenius Number

TL;DR

A new algorithm to calculate the Frobenius number is presented and the sequential form of the new algorithm is presented.

Abstract

A number has a representation with respect to the numbers , if there exist the non-negative integers such that . The largest natural number that does not have a representation with respect to the numbers is called the Frobenius number and is denoted by the symbol . In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm.
Paper Structure (3 sections, 2 theorems, 16 equations, 1 table, 2 algorithms)

This paper contains 3 sections, 2 theorems, 16 equations, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. New algorithm
  3. The sequential form of algorithm

Key Result

Theorem 2.1

For the numbers $\alpha_1<\alpha_2<...<\alpha_n$, we have

Theorems & Definitions (4)

  • Theorem 2.1
  • proof
  • Theorem 3.1
  • Remark 3.2