1024.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 1024

References:

erdosproblems.com/1024
[PhRo86] Phelps, K. T. and R"odl, V., Steiner triple systems with minimum independence number. Ars Combin. (1986), 167--172.

Imports (1)

FormalConjecturesUtil

theorem Erdos1024.erdos_1024 Let $f(n)$ be such that every $3$-uniform linear hypergraph on $n$ vertices contains an independent set on $f(n)$ vertices sorry line 42 source
Source documentation
Let $f(n)$ be such that every $3$-uniform linear hypergraph on $n$ vertices contains an independent set on $f(n)$ vertices. Estimate $f(n)$.
Phelps and Rödl [PhRo86] proved $f(n) \asymp (n\log n)^{1/2}$.

depends on sorry what this means
Statement uses: Asymptotics.IsTheta, Nat, Real, Filter.atTop, Hypergraph.linearIndependenceNumber, Real.sqrt, HMul.hMul, Real.log
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
13 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1024 :
    (fun n ↦ (Hypergraph.linearIndependenceNumber n : ℝ)) =Θ[atTop]
    (answer(fun n : ℕ ↦ Real.sqrt (n * Real.log n)) : ℕ → ℝ) := by
…
```
Mentions: Hypergraph.linearIndependenceNumber