Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:application |
coloring problems
additive combinatorics |
| gptkbp:defines |
The largest n such that the numbers 1 to n can be colored with k colors without monochromatic solution to x + y = z
|
| gptkbp:describes |
partitioning of natural numbers
|
| gptkbp:field |
gptkb:mathematics
combinatorics |
| gptkbp:generalizes |
gptkb:sum-free_partition_problem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schur number
|
| gptkbp:introducedIn |
1916
|
| gptkbp:namedAfter |
gptkb:Issai_Schur
|
| gptkbp:notation |
S(k)
|
| gptkbp:OEIS |
A045652
|
| gptkbp:openProblem |
Exact values for S(6) and higher are unknown
|
| gptkbp:relatedTo |
gptkb:Ramsey_theory
partition regularity sum-free sets |
| gptkbp:S(1) |
1
|
| gptkbp:S(2) |
4
|
| gptkbp:S(3) |
13
|
| gptkbp:S(4) |
44
|
| gptkbp:S(5) |
161
|
| gptkbp:sequence |
1, 4, 13, 44, 161, ...
|
| gptkbp:studiedBy |
gptkb:Issai_Schur
|
| gptkbp:bfsParent |
gptkb:Schur's_theorem
|
| gptkbp:bfsLayer |
7
|