Source-pinned research
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This index contains 2,569 research declarations. Search 10,000 more complete Mathlib declarations.
2569 results
AbstractHeckeOperator.eq_finsum_quotient_out_of_bijOn'
Plain-language statement
If a is fixed by V then ∑ᶠ g ∈ s, g • a is independent of the choice s of coset representatives in G for a subset of G ⧸ V
Source project: Fermat's Last Theorem
Person-level attribution pending.
acc_lang_congr
Plain-language statement
The language accepted by c.toDA with a unique accepting state s is exactly the equivalence class of s.
Source project: Automata Theory
Person-level attribution pending.
AddDissociated.boringEnergy_le
Project documentation
If a finite set is additively dissociated, then its order- additive energy is at most , where is the project's Chang constant. This is the quantitative dissociated-set estimate used in the proof of Chang's lemma.
Source project: Arithmetic Progressions Almost Periodicity
Person-level attribution pending.
AddWriterT.expectedCostNat_eq_sum_tail_probs_of_pathwiseCostAtMost
Plain-language statement
Finite tail-sum formula for natural-valued writer cost under a pathwise upper bound. If every execution path of oa incurs cost at most n, then the tail probabilities vanish above n, so the infinite tail sum truncates to Finset.range n.
Source project: VCVio
Person-level attribution pending.
adiabatic_relation_log
Plain-language statement
Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.
Source project: Physlib
Person-level attribution pending.
adiabatic_relation_UaUbVaVb
Plain-language statement
Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.
Source project: Physlib
Person-level attribution pending.