Majority inputs of signed conjunction summaries

For a two-variable signed conjunction, false is its three-to-one majority output. A family has disjoint primary pairs when its endpoint map is injective.

def Algebraic.Cutwidth.Aggregate.Geometry.Fiber.endpoint {E : Type u_1} {V : Type u_2} (edge : E → Entropy.SignedEdge V) (p : E × Bool) : V

The two primary endpoints of every selected signed conjunction.

Equations

• Algebraic.Cutwidth.Aggregate.Geometry.Fiber.endpoint edge p = if p.2 = true then (edge p.1).right else (edge p.1).left

noncomputable def Algebraic.Cutwidth.Aggregate.Geometry.Fiber.majorityInputs {E : Type u_1} {V : Type u_2} [Fintype E] [Fintype V] (edge : E → Entropy.SignedEdge V) : Finset (V → Bool)

Inputs on which every selected conjunction takes its majority output.

Equations

• Algebraic.Cutwidth.Aggregate.Geometry.Fiber.majorityInputs edge = {x : V → Bool | ∀ (e : E), (edge e).eval x = false}