901.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 901

References:

erdosproblems.com/901
[Be77] Beck, J., On a combinatorial problem of {P}. {E}rdős and {L}. {L}ovász. Discrete Math. (1977), 127--131.
[Be78] Beck, J., On {$3$}-chromatic hypergraphs. Discrete Math. (1978), 127--137.
[Er63b] Erdős, P., On a combinatorial problem. Nordisk Mat. Tidskr. (1963), 5--10, 40.
[Er64e] Erdős, P., On a combinatorial problem. {II}. Acta Math. Acad. Sci. Hungar. (1964), 445--447.
[ErLo75] Erdős, P. and Lovász, L., Problems and results on {$3$}-chromatic hypergraphs and some related questions. (1975), 609--627.
[Pl09] Pluhár, András, Greedy colorings of uniform hypergraphs. Random Structures Algorithms (2009), 216--221.
[RaSr00] Radhakrishnan, Jaikumar and Srinivasan, Aravind, Improved bounds and algorithms for hypergraph {$2$}-coloring. Random Structures Algorithms (2000), 4--32.

Imports (1)

FormalConjecturesUtil

theorem Erdos901.erdos_901 Let $m(n)$ be minimal such that there is an $n$-uniform hypergraph with $m(n)$ edges which is $3$-chromatic sorry line 50 source
Source documentation
Let $m(n)$ be minimal such that there is an $n$-uniform hypergraph with $m(n)$ edges which is $3$-chromatic. Estimate $m(n)$.

depends on sorry what this means
Statement uses: Asymptotics.IsTheta, Nat, Real, Filter.atTop, ENat.toNat, Hypergraph.minChromaticEdges, OfNat.ofNat, sorryAx, Bool.false
Proof uses: Lean.Name, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_901 :
    (fun n ↦ ((Hypergraph.minChromaticEdges n 3).toNat : ℝ)) =Θ[atTop]
    (answer(sorry) : ℕ → ℝ) := by
…
```
Mentions: Hypergraph.minChromaticEdges