• Corpus ID: 246015496

Erd\H{o}s' minimum overlap problem

@inproceedings{White2022ErdHosMO,
  title={Erd\H\{o\}s' minimum overlap problem},
  author={E. P. White},
  year={2022}
}
  • E. White
  • Published 14 January 2022
  • Mathematics
We obtain a substantially improved lower bound for the minimum overlap problem asked by Erdős. Our approach uses elementary Fourier analysis to translate the problem to a convex optimization program. 

Figures and Tables from this paper

References

SHOWING 1-9 OF 9 REFERENCES

Advances in the Minimum Overlap Problem

Abstract Given any positive integer n , consider partitions of the integers 1, 2, …, 2 n into two disjoint classes { a i } and { b i } with n elements in each class. Denote by M k the number of

Unsolved problems in number theory

TLDR
The topics covered are: additive representation functions, the Erdős-Fuchs theorem, multiplicative problems (involving general sequences), additive and multiplicative Sidon sets, hybrid problems (i.e., problems involving both special and general sequences, arithmetic functions and the greatest prime factor func- tion and mixed problems.

The minimum overlap problem revisited

For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference between an element of A

Applications of Second Order Cone Programming

TLDR
A significant special case of the problems which could be solved were those whose constraints were given by semidefinite cones, and these have a wide range of applications, some of which are discussed in Section 5, and can still be solved efficiently using interior point methods.

On the minimal overlap problem of Erdös

The Accuracy of Floating Point Summation

  • N. Higham
  • Computer Science
    SIAM J. Sci. Comput.
  • 1993
TLDR
Five summation methods and their variations are analyzed here and no one method is uniformly more accurate than the others, but some guidelines are given on the choice of method in particular cases.

Some remarks on number theory (Hebrew, English summary)

  • Riveon Lematematika,
  • 1955