Vela Mathematics Program: problems

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285 problems · 6/6Number SourcesGraph view

declared openerdos:1122

Erdős problem 1122

number theoryN/A

declared openerdos:1131

Erdős problem 1131

analysispolynomialsN/A2 sources

declared openerdos:1132

Erdős problem 1132

analysispolynomialsN/A2 sources

declared openerdos:1143

Erdős problem 1143

number theoryprimesN/A2 sources

declared openerdos:1144

Erdős problem 1144

number theoryprobabilityN/A

declared openerdos:1151

Let

\mathcal{L}^nf

be the Lagrange interpolation polynomials of a continuous

f

on the Chebyshev nodes. Prove that, for any closed

A\subseteq [-1,1]

, there exists a continuous function

f

such that

A

is the set of limit points of

\mathcal{L}^nf(x)

analysispolynomialsN/A3 sources

declared openerdos:1152

Erdős problem 1152

analysispolynomialsN/A

declared openerdos:1155

Erdős problem 1155

graph theoryN/A

declared openerdos:1156

Erdős problem 1156

graph theorychromatic numberN/A

declared openerdos:1157

Erdős problem 1157

hypergraphsturan numberpossible

declared openerdos:1158

Erdős problem 1158

hypergraphsturan numberpossible

declared openerdos:1159

Erdős problem 1159

combinatoricsN/A

declared openerdos:1160

Erdős problem 1160

group theoryA000001

declared openerdos:1162

Erdős problem 1162

group theorypossible

declared openerdos:1163

Erdős problem 1163

group theoryN/A

declared openerdos:1168

Erdős problem 1168

set theoryramsey theoryN/A

declared openerdos:1170

Erdős problem 1170

set theoryramsey theoryN/A

declared openerdos:1171

Erdős problem 1171

set theoryramsey theoryN/A

declared openerdos:1172

Erdős problem 1172

set theoryramsey theoryN/A

declared openerdos:1173

Erdős problem 1173

set theorycombinatoricsN/A

declared openerdos:1177

For a finite forbidden triple system

G

, what exact uncountable chromatic cardinalities occur among

G

-free triple systems, and how do those spectra interact? The revised manuscript answers the three exact-cardinal questions and claims a complete spectrum dichotomy.

set theorychromatic numberhypergraphsN/A3 sources

declared openerdos:1178

Erdős problem 1178

graph theoryhypergraphsN/A

declared openerdos:1181

Erdős problem 1181

number theorypossible

declared openerdos:1182

Erdős problem 1182

graph theoryramsey theorypossible

declared openerdos:1183

Erdős problem 1183

combinatoricsramsey theorypossible2 sources

declared openerdos:1184

Erdős problem 1184

number theoryprimespossible

declared openerdos:1186

What is the minimum asymptotic density

\delta_k

of monochromatic

k

-term arithmetic progressions in every two-colouring of

\{1, \dots, n\}

? The exact certificate gives

\delta_3 = 117/2192

, matching the known 548-bead colouring.

additive combinatoricsarithmetic progressionspossible2 sources

declared openerdos:1189

For irreducible covering sets of size

k

, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.

number theorycovering systemspossible2 sources

declared open · $1000erdos:1191

Erdős problem 1191

additive combinatoricssidon setspossible

declared openerdos:1194

Erdős problem 1194

additive combinatoricsadditive basissidon setspossible2 sources

declared openerdos:1200

Erdős problem 1200

number theoryprimespossible

declared openerdos:1204

Erdős problem 1204

number theoryA008407 · A023193 · A135311 · possible

declared openerdos:1206

Erdős problem 1206

number theorysidon setspossible

declared openerdos:1207

Erdős problem 1207

geometrydistancespossible

declared openerdos:1208

Erdős problem 1208

geometrydistancesA193838 · A271490 · possible2 sources

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