# On a transport problem and monoids of non-negative integers

On a transport problem and monoids of non-negative integers A problem about how to transport profitably a group of cars leads us to studying the set T formed by the integers n such that the system of inequalities, with non-negative integer coefficients, \begin{aligned} a_1x_1 +\cdots + a_px_p + \alpha \le n \le b_1x_1 +\cdots + b_px_p - \beta \end{aligned} a 1 x 1 + ⋯ + a p x p + α ≤ n ≤ b 1 x 1 + ⋯ + b p x p - β has at least one solution in $${\mathbb N}^p$$ N p . We prove that $$T\cup \{0\}$$ T ∪ { 0 } is a submonoid of $$({\mathbb N},+)$$ ( N , + ) and, moreover, we give algorithmic processes to compute T. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png aequationes mathematicae Springer Journals

# On a transport problem and monoids of non-negative integers

, Volume 92 (4) – Jun 5, 2018
10 pages

/lp/springer_journal/on-a-transport-problem-and-monoids-of-non-negative-integers-WlZ8KvYK5O
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Combinatorics
ISSN
0001-9054
eISSN
1420-8903
D.O.I.
10.1007/s00010-018-0572-5
Publisher site
See Article on Publisher Site

### Abstract

A problem about how to transport profitably a group of cars leads us to studying the set T formed by the integers n such that the system of inequalities, with non-negative integer coefficients, \begin{aligned} a_1x_1 +\cdots + a_px_p + \alpha \le n \le b_1x_1 +\cdots + b_px_p - \beta \end{aligned} a 1 x 1 + ⋯ + a p x p + α ≤ n ≤ b 1 x 1 + ⋯ + b p x p - β has at least one solution in $${\mathbb N}^p$$ N p . We prove that $$T\cup \{0\}$$ T ∪ { 0 } is a submonoid of $$({\mathbb N},+)$$ ( N , + ) and, moreover, we give algorithmic processes to compute T.

### Journal

aequationes mathematicaeSpringer Journals

Published: Jun 5, 2018

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