Vela Mathematics Program: problems

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285 problems · 3/6Number SourcesGraph view

declared openerdos:571

Erdős problem 571

graph theoryturan numberN/A

declared openerdos:572

Erdős problem 572

graph theoryturan numberpossible

declared openerdos:573

Erdős problem 573

graph theoryturan numberA006856

declared openerdos:575

Erdős problem 575

graph theoryturan numberN/A

declared openerdos:576

Erdős problem 576

graph theoryturan numberpossible

declared openerdos:584

Must every graph with

n

vertices and

\delta n^2

edges contain large subgraphs in which every two edges lie on specified short cycles? A dense high-girth construction refutes the statement when

\delta

may shrink with

n

graph theorycyclesN/A2 sources

declared openerdos:585

Erdős problem 585

graph theorycyclespossible

declared open · $100erdos:588

Erdős problem 588

geometryA006065 · A008997

declared openerdos:589

Erdős problem 589

geometrypossible

declared openerdos:597

Erdős problem 597

graph theoryramsey theoryset theoryN/A

declared open · $500erdos:601

Erdős problem 601

graph theoryset theoryN/A

declared open · $500erdos:604

Erdős problem 604

geometrydistancespossible

declared openerdos:609

Erdős problem 609

graph theoryramsey theorypossible

declared openerdos:611

Erdős problem 611

graph theoryN/A

declared openerdos:612

Erdős problem 612

graph theoryN/A

declared openerdos:614

Erdős problem 614

graph theorypossible

declared openerdos:616

Erdős problem 616

graph theoryN/A2 sources

declared openerdos:620

Erdős problem 620

graph theorypossible

declared open · $1000erdos:625

Erdős problem 625

graph theorychromatic numberN/A

declared openerdos:626

Erdős problem 626

graph theorychromatic numbercyclespossible

declared openerdos:627

Erdős problem 627

graph theorychromatic numberpossible

declared openerdos:629

Erdős problem 629

graph theorychromatic numberpossible2 sources

declared open · $25erdos:634

Erdős problem 634

geometrypossible

declared openerdos:635

Erdős problem 635

number theoryN/A2 sources

declared openerdos:638

Erdős problem 638

graph theoryramsey theoryN/A

declared openerdos:640

Erdős problem 640

graph theorychromatic numberN/A

declared openerdos:642

Erdős problem 642

graph theorycyclespossible

declared openerdos:643

Erdős problem 643

graph theoryhypergraphspossible

declared openerdos:644

Erdős problem 644

combinatoricspossible

declared openerdos:654

n

planar points have no four concyclic, must some point determine

(1 - o(1))n

distinct distances? Failing that, can one always force more than

(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:663

Erdős problem 663

number theoryA391668

declared openerdos:665

Erdős problem 665

combinatoricsN/A2 sources

declared openerdos:667

Erdős problem 667

graph theoryramsey theoryN/A

declared openerdos:668

Erdős problem 668

geometrydistancesA385657

declared openerdos:669

Erdős problem 669

geometryA003035 · A006065 · A008997 · possible

declared openerdos:670

Erdős asked whether every

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 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 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 openerdos:691

Erdős problem 691

number theoryN/A

declared openerdos:693

Erdős problem 693

number theorydivisorsA391118 · possible

declared openerdos:704

Erdős problem 704

graph theorygeometrychromatic numberN/A

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