# Category:Transitive-symmetric function

## Definition

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

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).

## Subcategories

This category has only the following subcategory.

## Pages in category "Transitive-symmetric function"

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