Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:theorem
|
| gptkbp:application |
theoretical computer science
|
| gptkbp:appliesTo |
coloring problems
|
| gptkbp:causedBy |
combinatorial methods
|
| gptkbp:commanded |
For any given positive integers k and r, there exists a minimum number N such that if the integers 1 to N are colored with r colors, there will always be a monochromatic arithmetic progression of length k.
|
| gptkbp:condition |
If N is large enough, then a monochromatic arithmetic progression exists.
|
| gptkbp:established |
gptkb:Bertand_Van_der_Waerden
|
| gptkbp:examples |
For_k=3_and_r=2,_N=9_is_sufficient.
|
| gptkbp:field |
combinatorial mathematics
|
| gptkbp:hasRelatedPatent |
mathematical logic
|
| https://www.w3.org/2000/01/rdf-schema#label |
Van der Waerden's theorem
|
| gptkbp:influencedBy |
gptkb:Hilbert's_problems
|
| gptkbp:isActiveIn |
mathematical proofs
|
| gptkbp:isAttendedBy |
coloring examples
|
| gptkbp:isAvenueFor |
algorithm design
real-world problems. |
| gptkbp:isChallengedBy |
mathematical proofs
|
| gptkbp:isCitedBy |
gptkb:Bertand_Van_der_Waerden
|
| gptkbp:isCitedIn |
numerous mathematical papers
|
| gptkbp:isConnectedTo |
finite fields
|
| gptkbp:isConsidered |
theory of numbers
|
| gptkbp:isDescribedAs |
theoretical research
|
| gptkbp:isDiscussedIn |
academic conferences
|
| gptkbp:isExaminedBy |
research studies
textbooks on combinatorics |
| gptkbp:isExploredIn |
combinatorial optimization
computational methods |
| gptkbp:isFamousFor |
its implications in number theory
|
| gptkbp:isIncorporatedIn |
counterexamples
combinatorial proofs |
| gptkbp:isLinkedTo |
set theory
|
| gptkbp:isNotableFor |
its historical significance
|
| gptkbp:isNotedFor |
its combinatorial nature
|
| gptkbp:isPartOf |
mathematical analysis
combinatorial theory |
| gptkbp:isRecognizedBy |
mathematicians
|
| gptkbp:isReflectedIn |
mathematical literature
|
| gptkbp:isRelatedTo |
partition theory
discrete mathematics Szemerédi's theorem |
| gptkbp:isStudiedIn |
discrete mathematics
|
| gptkbp:isSupportedBy |
numerical evidence
|
| gptkbp:isTrainedIn |
various mathematical contexts
|
| gptkbp:isUsedIn |
graph theory
|
| gptkbp:isUtilizedFor |
arithmetic combinatorics
prove_for_large_k_and_r. |
| gptkbp:isUtilizedIn |
data analysis
|
| gptkbp:keyIssues |
understanding combinatorial structures
|
| gptkbp:knownFor |
Van_der_Waerden's_theorem_on_arithmetic_progressions
|
| gptkbp:publishedIn |
1930
|
| gptkbp:relatedPatent |
combinatorial number theory
coloring of integers arithmetic progression |
| gptkbp:relatedTo |
Ramsey_theory
|
| gptkbp:standardFeatures |
Roth's_theorem
|