论文标题
自2016年以来的一次性运输问题及其在1903年可能的解决方案
A Diophantine transport problem from 2016 and its possible solution in 1903
论文作者
论文摘要
我们是由最近的一次性运输问题激励的，该问题涉及如何运输一群人或物体，我们调查了关于解决非负整数中线性二氧甘氨酸方程式和不平等系统的经典事实。我们强调了1903年的埃利奥特（Elliott）方法，并由麦克马洪（Macmahon）在他的``$ω$ calculus''或分区分析中进一步开发。作为例证，我们根据几个变量的形式功率序列获得了所考虑的运输问题的解决方案，这是特殊形式的理性函数的扩展。
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 ``$Ω$-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.
