Theorems · Theorem · number theory
Finset.addEnergy_eq_sum_sq
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Add α] [inst_2 : Fintype α] (s t : Finset α),
s.addEnergy t = ∑ a, {xy ∈ s ×ˢ t | xy.1 + xy.2 = a}.card ^ 2- Defined in
- Mathlib.Combinatorics.Additive.Energy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddFintype
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Cites15
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
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.cardstatement and proof · cited by 2,327
- SProd.sprodstatement and proof · cited by 1,750
- Finset.filterstatement and proof · cited by 949
- Finset.mem_productproof · cited by 48
- Finset.card_eq_zeroproof · cited by 34
- Finset.addEnergystatement · cited by 21
- OfNat.ofNat_ne_zeroproof · cited by 20
- Finset.add_mem_addproof · cited by 12
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