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Results tagged with ramsey-theory
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user 74918
Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.
4
votes
1
answer
90
views
Ramsey style theorem with unbounded colors
Question: Let $\varepsilon>0$ and $N\in\omega$ be sufficiently large (depending on $\varepsilon$).
Let $h:\subseteq N\rightarrow N$ be such that $h(B)\notin B$ for all $B\subsetneq N$.
Must there be …
- 18.8k
1
vote
0
answers
138
views
A generalization of Hales-Jewett theorem
Hales-Jewett theorem ($HJ(\alpha,k,n)$) states that for every coloring $f:\alpha^N\rightarrow k$ where $N$ is sufficiently large, there is an $n$-dimensional combinatorial subspace of $\alpha^N$ that …
- 909
4
votes
0
answers
111
views
Set version of ramsey type problem
For two sets of numbers $A,B$, write $A<B$ iff $\max A<\min B$.
For a sequence of integers $a_0,\cdots,a_{n-1}>0$,
let $Prop(a_0,\cdots,a_{n-1})$ denote the following proposition:
Given $n$ sets of i …
- 909
6
votes
1
answer
349
views
Ramsey type theorem
Let $\mathcal{P}(\{0,\dotsc,7\})$ denote the power set of $\{0,\dotsc,7\}$.
Is the following true?
For any function $f: \mathcal{P}(\{0,\dotsc,7\})\rightarrow\{0,1\}$ there exists $0\leq k\leq 3$ …
- 12.4k