esymm_eq_sum_monomial — Mathlib

English

Esymm can be expressed as a sum over explicit monomials: esymm(σ,R,n) = ∑_{t ∈ powersetCard(n, univ)} monomial( ∑_{i∈t} Finsupp.single i 1 ) 1.

Русский

Esymm является суммой по явным мономам: esymm(σ,R,n) = ∑_{t ∈ powersetCard(n, univ)} мономиал( ∑_{i∈t} e_i ) 1.

LaTeX

$$$ esymm(\\sigma,R,n) = \\sum t \\in (\\mathrm{powersetCard}\\; n\\; \\mathrm{univ}), \\mathrm{monomial}\\Big( \\sum i \\in t, Finsupp.single i\,1 \\Big) 1 $$$

Lean4

/-- We can define `esymm σ R n` as a sum over explicit monomials -/
theorem esymm_eq_sum_monomial (n : ℕ) :
    esymm σ R n = ∑ t ∈ powersetCard n univ, monomial (∑ i ∈ t, Finsupp.single i 1) 1 := by
  simp_rw [monomial_sum_one, esymm, ← X_pow_eq_monomial, pow_one]

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