Theorems · Definition · number theory
addRothNumber
{α : Type u_2} → [DecidableEq α] → [AddMonoid α] → Finset α →o ℕThe additive Roth number of a finset is the cardinality of its biggest 3AP-free
subset.
The usual Roth number corresponds to addRothNumber (Finset.range n), see rothNumberNat.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- Finset.cardproof · cited by 2,327
- OrderHomstatement · cited by 934
- ThreeAPFreeproof · cited by 38
- Nat.findGreatestproof · cited by 25
Cited by21
Results whose statement or proof uses this declaration.
- rothNumberNatproof · cited by 17
- addRothNumber_specstatement · cited by 8
- ThreeAPFree.le_addRothNumberstatement · cited by 7
- addRothNumber_lestatement · cited by 3
- addRothNumber_map_add_leftstatement and proof · cited by 3
- IsAddFreimanHom.addRothNumber_monostatement and proof · cited by 2
- addRothNumber_emptystatement · cited by 1
- addRothNumber_le_ruzsaSzemerediNumberstatement and proof · cited by 1
- IsAddFreimanIso.addRothNumber_congrstatement and proof · cited by 1
- addRothNumber_union_lestatement and proof · cited by 1
- rothNumberNat_le_ruzsaSzemerediNumberNatproof · cited by 1
- ThreeAPFree.addRothNumber_eqstatement · cited by 1