Theorems · Definition · combinatorics
List.Nat.antidiagonalTuple
(k : ℕ) → ℕ → List (Fin k → ℕ)
List.antidiagonalTuple k n is a list of all k-tuples which sum to n.
This list contains no duplicates (List.Nat.nodup_antidiagonalTuple), and is sorted
lexicographically (List.Nat.antidiagonalTuple_pairwise_pi_lex), starting with ![0, ..., n]
and ending with ![n, ..., 0].
``
#eval antidiagonalTuple 3 2
-- [![0, 0, 2], ![0, 1, 1], ![0, 2, 0], ![1, 0, 1], ![1, 1, 0], ![2, 0, 0]]
``
- Defined in
- Mathlib.Data.Fin.Tuple.NatAntidiagonal
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext
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 by10
Results whose statement or proof uses this declaration.
- Multiset.Nat.antidiagonalTupleproof · cited by 7
- List.Nat.mem_antidiagonalTuplestatement and proof · cited by 2
- List.Nat.antidiagonalTuple_onestatement and proof · cited by 2
- List.Nat.nodup_antidiagonalTuplestatement and proof · cited by 1
- List.Nat.antidiagonalTuple_twostatement · cited by 1
- List.Nat.antidiagonalTuple_zero_rightstatement · cited by 1
- List.Nat.antidiagonalTuple_zero_succstatement · cited by 1
- List.Nat.antidiagonalTuple_zero_zerostatement · cited by 0
- List.Nat.antidiagonalTuple.eq_defstatement and proof · cited by 0
- List.Nat.antidiagonalTuple_pairwise_pi_lexstatement · cited by 0