Find the value of the limit of MinOverlapQuotient!
The quotient of the minimum maximum overlap $M(N)$ by $N$. The central question of the minimum overlap problem is to determine the asymptotic behavior of this quotient as $N \to \infty$. -/ noncomputable def MinOverlapQuotient (N : ℕ) := (M N : ℝ) / N
/-- A lower bound of $\frac 1 4$. See Some remarks on number theory (in Hebrew) by Paul Erdős, Riveon Lematematika 9, p.45-48,1955
A lower bound of $1 - frac{1}{\sqrt 2}$. Scherk (written communication), see On the minimal overlap problem of Erdös by Leo Moser, Аста Аrithmetica V, p. 117-119, 1959
A lower bound of $\frac{4 - \sqrt{6}}{5}. See On the intersection of a linear set with the translation of its complement by Stanisław Świerczkowski1, Colloquium Mathematicum 5(2), p. 185-197, 1958
A lower bound of $\sqrt{4 - \sqrt{15}}$.
A lower bound of $0.379005$. See Erdős' minimum overlap problem by Ethan Patrick White, 2022
The example (with $N$ even), $A = {\frac N 2 + 1, \dots, \frac{3N}{2}}$ shows an upper bound of $\frac 1 2$.
An upper bound of $\frac 2 5$. See Minimal overlapping under translation. by T. S. Motzkin, K. E. Ralston and J. L. Selfridge, in "The summer meeting in Seattle" by V. L. Klee Jr., Bull. Amer. Math. Soc.62, p. 558, 1956
An upper bound of $0.38200298812318988$. See Advances in the Minimum Overlap Problem by Jan Kristian Haugland, Journal of Number Theory Volume 58, Issue 1, p 71-78, 1996
An upper bound of $0.3809268534330870$. See The minimum overlap problem by Jan Kristian Haugland
Find a better lower bound!
Find a better upper bound!
The limit of MinOverlapQuotient exists and it is less than $0.385694$.
minimum overlap problem