# Category:Transitive-symmetric function

## Definition

A **transitive-symmetric Boolean function** is a Boolean function [math]f:\{-1,1\}^n \to \{-1,1\}[/math] with the following property: For every two input bits [math]i[/math] and [math]j[/math], there exists a permutation [math]\sigma[/math] with [math]\sigma(i) = j[/math] so that [math]f(x) = f(\sigma(x))[/math].

Informally, a transitive-symmetric Boolean function where every two bits are treated equally.

## Properties

- Every symmetric Boolean function is transitive-symmetric, but not vice versa (for example, the Tribes function is transitive-symmetric but not symmetric).

## References

## Pages in category "Transitive-symmetric function"

The following 4 pages are in this category, out of 4 total.