Geodesic
A Diophantine transport problem from 2016 and its possible solution from 1903
Mathematics and Education in Mathematics, Tome 49 (2020), pp. 89-113.

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Motivated by a recent Diophantine transport problem about how to transport prof- itably 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 development 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. Този проект е мотивиран от неотдавнашен диофантов транспортен проблем как да транспортираме изгодно група от хора или обекти. Ние правим обзор на класически факти за решаване на системи линейни диофантови уравнения и неравенства в неотрицателни цели числа. Специално внимание отделяме на ме- тода на Елиът от 1903 година и неговото по-нататъшно развитие от МакМахън в неговото ”Омега смятане“. Като илюстрация намираме решение на разглеж- дания транспортен проблем на езика на формални степенни редове на няколко променливи, които са развития на рационални функции от специален вид.
Keywords: Linear Diophantine inequalities, solutions in nonnegative integers, transport problem, generating functions, Laurent series, nice rational functions, 11D75, 11D72, 11Y50, 05A15, 30B10, 32A05, 90B06, 90C08, линейни диофантови уравнения, решения в неотрицателни цели числа, транспортна задача, генериращи функции, Лоранов ред, хубави рационални функции, 11D75, 11D72, 11Y50, 05A15, 30B10, 32A05, 90B06, 90C08 
@article{MEM_2020_49_a9,
     author = {Boumova, Silvia and Drensky, Vesselin and Kostadinov, Boyan},
     title = {A {Diophantine} transport problem from 2016 and its possible solution from 1903},
     journal = {Mathematics and Education in Mathematics},
     pages = {89--113},
     publisher = {mathdoc},
     volume = {49},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2020_49_a9/}
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Boumova, Silvia; Drensky, Vesselin; Kostadinov, Boyan. A Diophantine transport problem from 2016 and its possible solution from 1903. Mathematics and Education in Mathematics, Tome 49 (2020), pp. 89-113. http://geodesic.mathdoc.fr/item/MEM_2020_49_a9/