Vela Mathematics Program: problems

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285 problems · 5/6Number SourcesGraph view

declared openerdos:876

Erdős problem 876

additive combinatoricsN/A

declared openerdos:878

Erdős problem 878

number theoryA339378 · possible

declared openerdos:879

Erdős problem 879

number theoryA186736

declared openerdos:883

Erdős problem 883

number theorygraph theoryN/A

declared openerdos:892

Erdős problem 892

number theoryprimitive setsN/A

declared openerdos:901

Erdős problem 901

combinatoricshypergraphspossible

declared openerdos:902

Erdős problem 902

graph theoryA362137

declared openerdos:911

Erdős problem 911

graph theoryramsey theoryN/A

declared openerdos:917

Erdős problem 917

graph theorychromatic numberN/A

declared openerdos:919

Erdős problem 919

graph theorychromatic numberN/A

declared openerdos:928

Erdős problem 928

number theoryA006530

declared openerdos:929

Erdős problem 929

number theorypossible

declared openerdos:934

Erdős problem 934

graph theorypossible

declared openerdos:935

Erdős problem 935

number theoryA057521 · A389244 · possible2 sources

declared openerdos:953

What is the largest possible measure of a subset of a radius-

R

disk in

\mathbb{R}^2

containing no pair of points at a positive integer distance? A Poisson-Bessel kernel argument gives

M(R) \ll R^{1/2}

; with Sárközy's lower construction,

M(R) = R^{1/2 + o(1)}

geometrydistancesN/A3 sources

declared openerdos:954

Erdős problem 954

number theoryA3906422 sources

declared openerdos:956

Erdős problem 956

geometrydistancesconvexpossible2 sources

declared openerdos:963

Erdős problem 963

number theorypossible2 sources

declared openerdos:969

Erdős problem 969

number theoryA0139282 sources

declared openerdos:970

Erdős problem 970

number theoryA048669

declared openerdos:976

Erdős problem 976

number theoryN/A2 sources

declared openerdos:983

Erdős problem 983

number theorypossible2 sources

declared openerdos:995

Erdős problem 995

analysisdiscrepancyN/A2 sources

declared openerdos:1005

Erdős problem 1005

number theoryA386893

declared openerdos:1011

Erdős problem 1011

graph theorypossible

declared openerdos:1013

Erdős problem 1013

graph theoryA292528

declared openerdos:1016

Erdős problem 1016

graph theorycyclesA105206

declared openerdos:1017

Erdős problem 1017

graph theorypossible

declared open · $100erdos:1029

Erdős problem 1029

graph theoryramsey theoryA059442

declared openerdos:1030

Erdős problem 1030

graph theoryramsey theoryA000791 · A059442

declared openerdos:1032

Do arbitrarily large 4-chromatic edge-critical graphs exist with minimum degree bounded below by a positive constant times the number of vertices?

graph theorychromatic numberpossible3 sources

declared openerdos:1033

Erdős problem 1033

graph theorypossible2 sources

declared openerdos:1035

Erdős problem 1035

graph theorypossible

declared openerdos:1039

For

f(z) = \prod_{i=1}^n (z - z_i)

with all

|z_i| \le 1

, let

\rho(f)

be the radius of the largest disc contained in

\{z : |f(z)| < 1\}

. Is

\rho(f) \gg 1/n

? The worst case is now known to be

\Theta(1/n)

, with the explicit bound

\rho(f) \ge (\log 2)/n

analysisN/A3 sources

declared openerdos:1040

For a closed infinite set

F \subseteq \mathbb{C}

, let

\mu(F)

be the infimum of

|\{z : |f(z)| < 1\}|

over monic polynomials with zeros in

F

. Is

\mu(F)

determined only by the transfinite diameter of

F

analysisN/A3 sources

declared openerdos:1045

Erdős problem 1045

analysisN/A

declared openerdos:1053

Erdős problem 1053

number theoryA007539

declared openerdos:1066

Erdős problem 1066

graph theoryplanar graphspossible

declared openerdos:1070

Erdős problem 1070

geometrypossible2 sources

declared openerdos:1075

Erdős problem 1075

hypergraphsN/A

declared openerdos:1083

Erdős problem 1083

geometrydistancesA186704 · possible

declared openerdos:1086

Erdős problem 1086

geometrydistancespossible

declared openerdos:1087

Erdős problem 1087

geometrydistancespossible

declared openerdos:1088

Erdős problem 1088

geometrypossible

declared openerdos:1100

Erdős problem 1100

number theorydivisorsA325864 · possible2 sources

declared openerdos:1103

Erdős problem 1103

number theoryA392164

declared openerdos:1109

Erdős problem 1109

number theoryA392164 · A392165

declared openerdos:1111

Erdős problem 1111

graph theorypossible

declared openerdos:1117

Erdős problem 1117

analysisN/A

declared openerdos:1120

Erdős problem 1120

analysisN/A

Problems · Vela Mathematics Program

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