You are here
Homealphabet
Primary tabs
alphabet
An alphabet $\Sigma$ is a nonempty finite set such that every string formed by elements of $\Sigma$ can be decomposed uniquely into elements of $\Sigma$.
For example, $\{b,lo,g,bl,og\}$ is not a valid alphabet because the string $blog$ can be broken up in two ways: b lo g and bl og. $\{\mathbb{C}a,\ddot{n}a,{\rm d},a\}$ is a valid alphabet, because there is only one way to fully break up any given string formed from it.
If $\Sigma$ is our alphabet and $n\in\mathbb{Z}^{+}$, we define the following as the powers of $\Sigma$:

$\Sigma^{0}={\lambda}$, where $\lambda$ stands for the empty string.

$\Sigma^{n}=\{xyx\in\Sigma,y\in\Sigma^{{n1}}\}$ ($xy$ is the juxtaposition of $x$ and $y$)
Related:
KleeneStar, Substring, Language, HuffmanCoding, Word
Synonym:
powers of an alphabet
Type of Math Object:
Definition
Major Section:
Reference
Mathematics Subject Classification
03C07 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
Sep 28
new question: how to contest an entry? by zorba
new question: simple question by parag
Sep 26
new question: Latent variable by adam_reith
Sep 17
new question: Harshad Number by pspss
Sep 14
new problem: Geometry by parag
new question: how to contest an entry? by zorba
new question: simple question by parag
Sep 26
new question: Latent variable by adam_reith
Sep 17
new question: Harshad Number by pspss
Sep 14
new problem: Geometry by parag