Theorems · Theorem · number theory

Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted

∀ (R : Type u_1) [inst : CommRing R] [NoZeroDivisors R] {m : ℕ},
  0 < m →
    (PowerSeries.mk fun n => ↑(Nat.Partition.restricted n fun x => ¬m ∣ x).card) =
      PowerSeries.mk fun n => ↑(Nat.Partition.countRestricted n m).card

Defined in: Mathlib.Combinatorics.Enumerative.Partition.Glaisher
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing NoZeroDivisors

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites29

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpaceproof · cited by 24,529
CommRingstatement and proof · cited by 17,173
Finset.sumproof · cited by 5,195
Bot.botproof · cited by 4,720
Nontrivialproof · cited by 2,416
Finset.cardstatement and proof · cited by 2,327
Finset.sum_congrproof · cited by 2,323
SummationFilter.unconditionalproof · cited by 2,068
Finset.rangeproof · cited by 1,341
tsumproof · cited by 1,148
PowerSeriesstatement and proof · cited by 797
NoZeroDivisorsstatement and proof · cited by 545

Cited by1

Results whose statement or proof uses this declaration.

Nat.Partition.card_restricted_eq_card_countRestrictedproof · cited by 1