Limits of some combinatorial problems

We show some new examples how can limit theory help understanding combinatorial structures. We introduce two limit problems of Alpern's Caching Game, which are good approximations of the original game when some parameters tend to infinity. With the use of these limit problems, we show some surprising results which radically changes our expectations about the structure of the optimal solution, e.g. this disproves the Kikuta-Ruckle Conjecture for Caching Games. For another example, we generalize the Manickam–Miklós–Singhi Conjecture, using limit theory.