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 non-negative integers. We emphasize on the method of Elliott from 1903 and its further development by MacMahon in his ‘Ω-Calculus’ or Partition Analysis. Then we show how this approach can be used to solve problems in classical and non-commutative invariant theory and theory of algebras with polynomial identities.
The obtained results are due to a big team of mathematicians in Bulgaria, Italy, Turkey and Hungary. The talk is a joint project with Silvia Boumova.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
