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Rademacher sign of a Boolean coloring

Definition
RSign

by xbgxjack · Sep 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

combinatoricsdiscrepancy-theory

Given a Boolean coloring χ:Fin m→{true,false}\chi:\mathrm{Fin}\,m\to\{\mathrm{true},\mathrm{false}\}χ:Finm→{true,false} and a coordinate jjj, RSign(χ,j)\mathrm{RSign}(\chi,j)RSign(χ,j) is the corresponding ±1\pm1±1 Rademacher value: +1+1+1 if χ(j)=true\chi(j)=\mathrm{true}χ(j)=true, and −1-1−1 otherwise. This is the standard translation between a Boolean coloring and a {−1,+1}\{-1,+1\}{−1,+1}-valued sign vector used throughout discrepancy theory.

Definition code
import Mathlib

def RSign {m : ℕ} (χ : Fin m → Bool) (j : Fin m) : ℝ :=
  if χ j then 1 else -1
Source
J. Spencer, "Six standard deviations suffice", Trans. Amer. Math. Soc. 289 (1985), 679-706.
Human review
  • Endorsed by Shuze Chen · Sep 11, 2026

  • Endorsed by xbgxjack · Sep 11, 2026

    Confirmed by the mission captain (proposal self-audit).

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