Claims › ext:63662d8a47d27642 › line of work
Its line of work
Whereas many hypergraph Ramsey numbers grow either at most polynomially or at least exponentially, we show that the off-diagonal Ramsey number $r(K_{4}^{(3)},S_n^{(3)})$ exhibits an unusual intermediate growth rate, namely, \[ 2^{c \log^2 n} \le r(K_{4}^{(3)},S_n^{(3)}) \le 2^{c' n^{2/3}\log n} \] for some positive constants $c$ and $c'$.
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Every claim drawn, as a table
| Claim | Status | Checkable | Credence | Use | Stakes | Rests on |
|---|---|---|---|---|---|---|
| Whereas many hypergraph Ramsey numbers grow either at most polynomially or at least exponentially, we show that the off… | ○ unchecked | yes | 0.55 | 0 | 1.6 | We prove general upper and lower bounds on $R(n;r,s)$ which imply that $R(n;r,s) = 2^{Θ(nr)}$ if $s/r$ is bounded away… |
| We prove general upper and lower bounds on $R(n;r,s)$ which imply that $R(n;r,s) = 2^{Θ(nr)}$ if $s/r$ is bounded away… | ○ unchecked | yes | 0.55 | 0 | 3.0 | — |
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Step by step
| Where | Status | Claim | Credence |
|---|---|---|---|
| 1 step below | unchecked | We prove general upper and lower bounds on $R(n;r,s)$ which imply that $R(n;r,s) = 2^{Θ(nr)}$ if $s/r$ is bounded away from $0$ and $1$.this claim takes its method from it, as the citing paper says · human literature · ext:ffc6cadb9a158fc4 | 0.55 |
| this claim | unchecked | Whereas many hypergraph Ramsey numbers grow either at most polynomially or at least exponentially, we show that the off-diagonal Ramsey number $r(K_{4}^{(3)},S…human literature · ext:63662d8a47d27642 | 0.55 |
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