Ellis–van der Waerden theorem
GPTKB entity
Statements (42)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
coloring of integers
|
| gptkbp:example |
a Ramsey-type theorem
|
| gptkbp:has_applications_in |
gptkb:computer_science
|
| gptkbp:has_expansion |
higher dimensions
various mathematicians |
| gptkbp:has_implications_for |
number theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ellis–van der Waerden theorem
|
| gptkbp:involves |
finite sets
|
| gptkbp:is_a_classic_result_in |
the field of mathematics
|
| gptkbp:is_a_foundation_for |
the study of patterns in numbers
|
| gptkbp:is_a_foundational_result_in |
combinatorial theory
|
| gptkbp:is_a_subject_of |
gptkb:Mathematician
mathematical research |
| gptkbp:is_applicable_to |
finite colorings
|
| gptkbp:is_cited_in |
mathematical literature
|
| gptkbp:is_connected_to |
Hilbert's basis theorem
|
| gptkbp:is_discussed_in |
combinatorial optimization
|
| gptkbp:is_often_discussed_in |
the Erdős– Szekeres theorem
|
| gptkbp:is_often_referenced_in |
gptkb:educational_materials
|
| gptkbp:is_part_of |
the curriculum in advanced mathematics courses
|
| gptkbp:is_related_to |
combinatorial number theory
the study of sequences and series partition regularity the van der Waerden conjecture |
| gptkbp:is_significant_for |
the study of sequences
|
| gptkbp:is_standardized_by |
Rado's theorem
|
| gptkbp:is_studied_in |
graph theory
|
| gptkbp:is_used_in |
Ramsey theory
|
| gptkbp:is_used_to_prove |
other combinatorial results
|
| gptkbp:issues |
combinatorial mathematics
|
| gptkbp:key |
additive combinatorics
|
| gptkbp:legal_principle |
has been influential in various mathematical fields.
|
| gptkbp:named_after |
gptkb:Alexander_van_der_Waerden
gptkb:Hermann_Weyl Bertlmann Ellis |
| gptkbp:provides |
conditions for monochromatic arithmetic progressions
|
| gptkbp:state |
for any given integers k and r, there exists a minimum number N such that any r-coloring of the integers {1, 2, ..., N} contains a monochromatic arithmetic progression of length k.
|
| gptkbp:was_a_result_of |
discrete mathematics
|
| gptkbp:was_proven_in |
gptkb:1927
|
| gptkbp:bfsParent |
gptkb:James_Ellis
|
| gptkbp:bfsLayer |
7
|