Vela Mathematics Program: problems

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613 problems · 7/13Number SourcesGraph view

declared openerdos:669

geometryA003035 · A006065 · A008997 · possible

declared openerdos:670

n

-point set in Euclidean space whose pairwise distances are mutually at least 1 apart must have diameter at least

(1+o(1))n^2

. Disproved: an explicit high-dimensional construction beats the conjectured constant.

geometrydistancesN/A2 sources

declared open · $250erdos:671

For triangular arrays of nodes

a_i^n\in[-1,1]

let

\mathcal{L}^nf

be the Lagrange interpolation polynomials of a continuous

f

, with fundamental polynomials

p_i^n

. Is there a choice of nodes such that for every continuous

f

there is some

x

where

\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty

and yet

\mathcal{L}^nf(x) \to f(x)

? Is there a choice with

\limsup_n \sum_i\lvert p_{i}^n(x)\rvert=\infty

for every

x

, yet for every continuous

f

some

x

has

\mathcal{L}^nf(x)\to f(x)

? Both questions are claimed resolved in the affirmative.

analysisN/A3 sources

declared provederdos:673

Erdős problem 673

number theorydivisorsN/A

declared openerdos:675

Erdős problem 675

number theoryN/A2 sources

declared openerdos:676

Erdős problem 676

number theoryA390181 · in progress

declared openerdos:679

Erdős problem 679

number theoryN/A2 sources

declared provederdos:682

Erdős problem 682

number theoryprimesA386978

declared openerdos:684

For the least

k

at which the small-prime part of

\binom{n}{k}

exceeds

n^2

, how large can

f(n)

be?

number theoryprimesbinomial coefficientsA392019 · possible3 sources

declared openerdos:685

Erdős problem 685

number theoryprimesbinomial coefficientsN/A

declared open · $1000erdos:687

Erdős problem 687

number theoryA048670 · A058989

declared solvederdos:690

Erdős problem 690

number theorypossible4 sources

declared openerdos:691

Erdős problem 691

number theoryN/A

declared openerdos:693

Erdős problem 693

number theorydivisorsA391118 · possible

declared solved (Lean)erdos:696

Erdős problem 696

number theorydivisorspossible4 sources

declared provederdos:702

Erdős problem 702

combinatoricsN/A

declared proved · $250erdos:703

Erdős problem 703

combinatoricsA390645

declared openerdos:704

Erdős problem 704

graph theorygeometrychromatic numberN/A

declared openerdos:706

Erdős problem 706

graph theorychromatic numberpossible

declared open · $100erdos:708

Erdős problem 708

number theorypossible

declared openerdos:709

How long must an interval be to contain distinct representatives

x_i

, with

a_i \mid x_i

, for every

n

-element set of moduli

A = \{a_1, \dots, a_n\}

number theorypossible2 sources

declared open · ₹2000erdos:710

Erdős problem 710

number theoryA390246

declared open · ₹1000erdos:711

Erdős problem 711

number theorypossible

declared open · $500erdos:712

Erdős problem 712

graph theoryturan numberhypergraphspossible

declared open · $500erdos:713

Erdős problem 713

graph theoryturan numberN/A

declared openerdos:714

Erdős problem 714

graph theoryturan numberpossible

declared provederdos:715

Erdős problem 715

graph theoryN/A

declared proved (Lean)erdos:716

Erdős problem 716

graph theoryhypergraphspossible3 sources

declared provederdos:717

Erdős problem 717

graph theoryN/A

declared provederdos:718

Erdős problem 718

graph theoryN/A

declared openerdos:719

Erdős problem 719

graph theoryhypergraphspossible

declared proved · $100erdos:720

Erdős problem 720

graph theoryramsey theorypossible

declared solvederdos:721

Erdős problem 721

number theoryadditive combinatoricsramsey theoryA171081

declared provederdos:722

Erdős problem 722

combinatoricsN/A

declared openerdos:724

Erdős problem 724

combinatoricsA001438

declared openerdos:725

Erdős problem 725

combinatoricsA001009

declared openerdos:731

Let

A(n)

be the least positive integer not dividing

\binom{2n}{n}

. Erdos asked for the behaviour of

A(n)

for reasonable

n

. Under an explicit dyadic-regularity formalization of reasonable, the distribution is determined on dyadic intervals against the scale

F_X = \sqrt{2}(\log 2)^{1/4} L^{1/4} \exp\sqrt{(\log 2)L}

with

L = \log(2X)

number theorybinomial coefficientsA0061974 sources

declared provederdos:732

Erdős problem 732

combinatoricsN/A

declared provederdos:733

Erdős problem 733

combinatoricsgeometrypossible

declared openerdos:734

Erdős problem 734

combinatoricspossible2 sources

declared solvederdos:735

Erdős problem 735

geometryN/A

declared not provableerdos:736

Erdős problem 736

graph theorychromatic numberN/A

declared provederdos:737

Erdős problem 737

graph theorychromatic numberN/A

declared openerdos:738

Erdős problem 738

graph theorychromatic numberN/A

declared not provableerdos:739

Erdős problem 739

graph theorychromatic numberN/A

declared falsifiableerdos:743

Erdős problem 743

graph theoryN/A2 sources

declared disprovederdos:744

Erdős problem 744

graph theorychromatic numberpossible

declared provederdos:745

Erdős problem 745

graph theoryN/A

declared provederdos:746

Erdős problem 746

graph theoryN/A

declared solvederdos:747

Erdős problem 747

combinatoricshypergraphsN/A

Problems · Vela Mathematics Program

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