A Diophantine transport problem from 2016 and its possible solution in 1903

Autor:	Boumova, Silvia, Drensky, Vesselin, Kostadinov, Boyan
Rok vydání:	2020
Předmět:	Mathematics - Number Theory Mathematics - Combinatorics Mathematics - Optimization and Control 11D75 11D72 11Y50 05A15 30B10 32A05 90B06 90C08
Zdroj:	Math. and Education in Math., Proc. of the Forty-ninth Spring Conf. of the Union of Bulgar. Mathematicians, 2020, 89-113
Druh dokumentu:	Working Paper
Popis:	Motivated by a recent Diophantine transport problem about how to transport profitably a group of persons or objects, we survey classical facts about solving systems of linear Diophantine equations and inequalities in nonnegative integers. We emphasize on the method of Elliott from 1903 and its further developed by MacMahon in his ``$\Omega$-Calculus'' or Partition Analysis. As an illustration we obtain the solution of the considered transport problem in terms of a formal power series in several variables which is an expansion of a rational function of a special form. Comment: Invited talk at Section A: Mathematical Structures" of the Forty Ninth Spring Conference of the Union of Bulgarian Mathematicians, 2020. To appear in "Mathematics and Education in Mathematics", 2020 Proceedings of the Forty Ninth Spring Conference of the Union of Bulgarian Mathematicians
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.06766 Zobrazit plný text záznamu View this record from Arxiv