Seven problems: so different yet close
The paper considers seven problems from linear algebra, combinatorics and a calendar-planning problem. Despite the apparent difference between these problems, the author shows that they have close connections. In Section 2, the seven problems are stated and extremum functions, which characterize the performance of the optimal solution in the worst case are presented. In Section 3, connections between the problems and relationships between the functions are analysed. In Section 4, further bounds on the functions are summarized, many of those referring to the literature, where the results originate. Section 5 provides concluding remarks, noting that problem P4 is central in the list of problems and three conjectures for further research are offered. For the entire collection see [Zbl 1476.68010].
scientific article; zbMATH DE number 7449711