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Problems · Vela Mathematics Program

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60 problems · 1/2NumberSourcesGraph view
declared proved · $500erdos:95
Erdős problem 95
geometryconvexdistancespossible
declared openerdos:102
Erdős problem 102
geometryN/A
declared openerdos:103
Erdős problem 103
geometrydistancespossible
declared open · $100erdos:104
Erdős problem 104
geometryA003829
declared falsifiableerdos:106
If f(n)f(n) is the maximum total side length of nn interior-disjoint squares packed in the unit square, is f(k2+1)=kf(k^2 + 1) = k? An exact rational configuration packs 1717 squares with total side length greater than 44, refuting the identity at k=4k = 4.
geometryN/A3 sources
declared disproved · $250erdos:135
Erdős problem 135
distancesgeometrypossible
declared openerdos:173
Erdős problem 173
geometryramsey theoryN/A
declared openerdos:174
Erdős problem 174
geometryramsey theoryN/A
declared provederdos:210
Erdős problem 210
geometryA003034
declared proved · $100erdos:211
Erdős problem 211
geometryN/A
declared provederdos:215
Erdős problem 215
geometryN/A
declared disprovederdos:216
Erdős problem 216
geometryconvexA381776
declared openerdos:217
Erdős problem 217
geometrydistancespossible
declared solvederdos:223
Erdős problem 223
geometrydistancespossible
declared provederdos:232
Erdős problem 232
geometrydistancesN/A
declared solvederdos:504
Erdős problem 504
geometryN/A
declared decidableerdos:506
Erdős problem 506
geometrypossible
declared solvederdos:526
Erdős problem 526
probabilitygeometryN/A
declared openerdos:528
Erdős problem 528
geometryA387897 · A156816
declared openerdos:529
Erdős problem 529
geometryprobabilityN/A
declared open · $100erdos:588
Erdős problem 588
geometryA006065 · A008997
declared openerdos:589
Erdős problem 589
geometrypossible
declared open · $500erdos:604
Erdős problem 604
geometrydistancespossible
declared provederdos:605
Erdős problem 605
geometrydistancespossible
declared solvederdos:606
Erdős problem 606
geometryN/A
declared proved · $250erdos:607
Erdős problem 607
geometrypossible
declared open · $25erdos:634
Erdős problem 634
geometrypossible
declared disprovederdos:651
Erdős problem 651
geometryconvexpossible
declared provederdos:652
Erdős problem 652
geometrydistancesN/A2 sources
declared openerdos:654
If nn planar points have no four concyclic, must some point determine (1−o(1))n(1 - o(1))n distinct distances? Failing that, can one always force more than (1/3+c)n(1/3 + c)n?
geometrydistancespossible3 sources
declared openerdos:657
Erdős problem 657
geometrydistancespossible
declared openerdos:660
Erdős problem 660
geometrydistancesconvexpossible
declared open · $50erdos:661
Erdős problem 661
geometrydistancespossible
declared openerdos:662
Among sufficiently large one-separated planar point sets, does the triangular lattice maximize the number of distances below each threshold? Explicit rational oblique lattices beat the triangular lattice under several closed- and strict-shell readings.
geometrydistancesN/A3 sources
declared openerdos:668
Erdős problem 668
geometrydistancesA385657
declared openerdos:669
Erdős problem 669
geometryA003035 · A006065 · A008997 · possible
declared openerdos:670
Erdős asked whether every nn-point set in Euclidean space whose pairwise distances are mutually at least 1 apart must have diameter at least (1+o(1))n2(1+o(1))n^2. Disproved: an explicit high-dimensional construction beats the conjectured constant.
geometrydistancesN/A2 sources
declared openerdos:704
Erdős problem 704
graph theorygeometrychromatic numberN/A
declared provederdos:733
Erdős problem 733
combinatoricsgeometrypossible
declared solvederdos:735
Erdős problem 735
geometryN/A
declared provederdos:754
Erdős problem 754
geometrydistancespossible
declared openerdos:827
Erdős problem 827
geometrypossible
declared openerdos:831
Erdős problem 831
geometrypossible
declared openerdos:838
Erdős problem 838
geometryconvexpossible
declared openerdos:953
What is the largest possible measure of a subset of a radius-RR disk in R2\mathbb{R}^2 containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives M(R)≪R1/2M(R) \ll R^{1/2}; with Sárközy's lower construction, M(R)=R1/2+o(1)M(R) = R^{1/2 + o(1)}.
geometrydistancesN/A3 sources
declared openerdos:956
Erdős problem 956
geometrydistancesconvexpossible2 sources
declared provederdos:957
Erdős problem 957
geometrydistancesN/A
declared disprovederdos:960
Erdős problem 960
geometrypossible3 sources
declared solvederdos:1069
Erdős problem 1069
geometrypossible
declared openerdos:1070
Erdős problem 1070
geometrypossible2 sources

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