Theorems · Definition · combinatorics
Sym
Type u_1 → ℕ → Type (max 0 u_1)
The nth symmetric power is n-tuples up to permutation. We define it
as a subtype of Multiset since these are well developed in the
library. We also give a definition Sym.sym' in terms of vectors, and we
show these are equivalent in Sym.symEquivSym'.
- Defined in
- Mathlib.Data.Sym.Basic
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 46 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- Multiset.cardproof · cited by 375
Cited by182
Results whose statement or proof uses this declaration.
- Sym.toMultisetstatement and proof · cited by 51
- Finset.symstatement · cited by 35
- Sym.consstatement and proof · cited by 26
- Sym.mapstatement and proof · cited by 22
- Sym.replicatestatement · cited by 15
- Sym.fillstatement and proof · cited by 11
- Sym.nilstatement · cited by 11
- List.symstatement · cited by 10
- Sym.attachstatement and proof · cited by 10
- Finset.mem_sym_iffstatement and proof · cited by 9
- Sym.coe_injectivestatement · cited by 8
- Sym.erasestatement and proof · cited by 8