77.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 77

References:

erdosproblems.com/77
[BBCGHMST24] Balister, P. and Bollobás, B. and Campos, M. and Griffiths, S. and Hurley, E. and Morris, R. and Sahasrabudhe, J. and Tiba, M., Upper bounds for multicolour Ramsey numbers. arXiv:2410.17197 (2024).
[CGMS23] Campos, Marcelo and Griffiths, Simon and Morris, Robert and Sahasrabudhe, Julian, An exponential improvement for diagonal Ramsey. arXiv:2303.09521 (2023).
[Er88] Erdős, P, Problems and results in combinatorial analysis and graph theory. Discrete Math. (1988), 81-92.
[Er93] Erdős, Paul, Some of my favorite solved and unsolved problems in graph theory. Quaestiones Math. (1993), 333-350.
[GNNW24] Gupta, P. and Ndiaye, N. and Norin, S. and Wei, L., Optimizing the CGMS upper bound on Ramsey numbers. arXiv:2407.19026 (2024).

Imports (1)

FormalConjecturesUtil

theorem Erdos77.erdos_77 Documented declaration: erdos_77 sorry line 52 source
Source documentation
If $R(k)$ is the Ramsey number for $K_k$, the minimal $n$ such that every $2$-colouring of the edges of $K_n$ contains a monochromatic copy of $K_k$, then find the value of $$\lim_{k\to \infty}R(k)^{1/k}.$$
This problem is #3 in Ramsey Theory in the graphs problem collection.

depends on sorry what this means
Statement uses: Filter.Tendsto, Nat, Real, HPow.hPow, SimpleGraph.diagonalRamsey, HDiv.hDiv, OfNat.ofNat, Filter.atTop, nhds, sorryAx, Bool.false
Proof uses: Lean.Name, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
27 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_77 :
    Filter.Tendsto (fun k : ℕ ↦ (SimpleGraph.diagonalRamsey k : ℝ) ^ (1 / (k : ℝ)))
      Filter.atTop (𝓝 answer(sorry)) := by
…
```
Mentions: SimpleGraph.diagonalRamsey