Theorems · Definition · number theory
List.IsZeckendorfRep
List ℕ → Prop
A list of natural numbers is a Zeckendorf representation (of a natural number) if it is an
increasing sequence of non-consecutive numbers greater than or equal to 2.
This is relevant for Zeckendorf's theorem, since if we write a natural n as a sum of Fibonacci
numbers (l.map fib).sum, IsZeckendorfRep l exactly means that we can't simplify any expression
of the form fib n + fib (n + 1) = fib (n + 2), fib 1 = fib 2 or fib 0 = 0 in the sum.
- Defined in
- Mathlib.Data.Nat.Fib.Zeckendorf
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by5
Results whose statement or proof uses this declaration.
- List.IsZeckendorfRep_nilstatement · cited by 0
- Nat.isZeckendorfRep_zeckendorfstatement and proof · cited by 0
- Nat.zeckendorfEquivstatement and proof · cited by 0
- List.IsZeckendorfRep.sum_fib_ltstatement and proof · cited by 0
- Nat.zeckendorf_sum_fibstatement and proof · cited by 0