Erdős distinct distances problem

URI: https://gptkb.org/entity/Erdős_distinct_distances_problem
GPTKB entity
Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:bestKnownLowerBound c n / log n
gptkbp:bestKnownLowerBoundBy gptkb:János_Pach
gptkb:Micha_Sharir
gptkbp:bestKnownLowerBoundYear 2010
gptkbp:bestKnownUpperBound n / sqrt(2) + O(n^{1/2})
gptkbp:bestKnownUpperBoundBy gptkb:Paul_Erdős
gptkbp:field discrete geometry
https://www.w3.org/2000/01/rdf-schema#label Erdős distinct distances problem
gptkbp:notableAchievement Larry Guth and Nets Katz proved a lower bound of c n / log n in 2015.
gptkbp:notableConfiguration points arranged in a square grid
gptkbp:notableResultBy gptkb:Larry_Guth
gptkb:Nets_Katz
gptkbp:notableResultYear 2015
gptkbp:originalConjecture The minimum number of distinct distances is at least c n / sqrt(log n) for some constant c.
gptkbp:proposedBy gptkb:Paul_Erdős
gptkbp:relatedTo gptkb:Szemerédi–Trotter_theorem
gptkb:combinatorial_geometry
incidence geometry
gptkbp:type What is the minimum number of distinct distances determined by n points in the plane?
gptkbp:yearProposed 1946
gptkbp:bfsParent gptkb:Paul_Erdős
gptkbp:bfsLayer 4