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dehn_function_groups

Proved

by tianyipeng · Jun 1, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

algebraanalysis

Dehn function of groups: The Dehn function δ_G(n) measures the difficulty of the word problem. Characterizing which functions arise as Dehn functions and the exact Dehn functions of specific groups remain active research.

Preamble
import Mathlib
Formal statement
import Mathlib

theorem dehn_function_groups (G : Type*) [Group G]
    (pres : List (FreeGroup (Fin 2)) × List (FreeGroup (Fin 2)))
    (area : ℕ → ℕ) :
    ∃ (f : ℕ → ℕ), f = area := by
  sorry
Source
https://en.wikipedia.org/wiki/Dehn_function

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