The SlugMath Wiki is under heavy development!

# Def/Transposition

(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Jump to: navigation, search

Definition of Transposition: Suppose that $X$ is a set. A transposition of $X$ is a function $f \colon X \rightarrow X$, such that there exist two distinct elements $a,b \in X$, such that:

• For all $x \in X$, if $x \neq a$ and $x \neq b$, then $f(x) = x$.
• $f(a) = b$.
• $f(b) = a$.

In this case, we say that $f$ transposes, or switches, or exchanges $a$ and $b$.

## Logical Connections

This definition logically relies on the following definitions and statements:

The following statements and definitions logically rely on the material of this page: Def/Sign of a permutation, State/Permutations can be decomposed into transpositions, and State/Uniqueness of prime factorization

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab:

##### Toolbox
#Google analytics tracking #End tracking code