Theorems · Definition · order theory
IncidenceAlgebra.zeta
(𝕜 : Type u_2) → {α : Type u_5} → [inst : Zero 𝕜] → [One 𝕜] → [inst_2 : LE α] → [DecidableLE α] → IncidenceAlgebra 𝕜 αThe zeta function of the incidence algebra is the function that assigns 1 to every nonempty interval, convolution with this function sums functions over intervals.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- ZeroOneLEDecidableLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IncidenceAlgebrastatement · cited by 51
Cited by11
Results whose statement or proof uses this declaration.
- IncidenceAlgebra.mu_mul_zetastatement and proof · cited by 3
- IncidenceAlgebra.mu_toDualproof · cited by 3
- IncidenceAlgebra.zeta_mul_mustatement and proof · cited by 2
- IncidenceAlgebra.zeta_applystatement · cited by 1
- IncidenceAlgebra.zeta_of_lestatement · cited by 1
- IncidenceAlgebra.zeta_prod_applystatement · cited by 1
- IncidenceAlgebra.zeta_prod_zetastatement · cited by 1
- IncidenceAlgebra.moebius_inversion_topproof · cited by 1
- IncidenceAlgebra.zeta_mul_zetastatement and proof · cited by 0
- IncidenceAlgebra.zeta_prod_mkstatement · cited by 0
- IncidenceAlgebra.mu_prod_muproof · cited by 0