Editing String (computer science) (section)

=== Concatenation and substrings ===
''[[Concatenation]]'' is an important [[binary operation]] on Σ<sup>*</sup>.  For any two strings ''s'' and ''t'' in Σ<sup>*</sup>, their concatenation is defined as the sequence of symbols in ''s'' followed by the sequence of characters in ''t'', and is denoted ''st''.  For example, if Σ = {a, b, ..., z}, ''s''&nbsp;=&nbsp;{{code|bear}}, and ''t''&nbsp;=&nbsp;{{code|hug}}, then ''st''&nbsp;=&nbsp;{{code|bearhug}} and ''ts''&nbsp;=&nbsp;{{code|hugbear}}.

String concatenation is an [[associative]], but non-[[commutative]] operation. The empty string ε serves as the [[identity element]]; for any string ''s'', ε''s'' = ''s''ε = ''s''.  Therefore, the set Σ<sup>*</sup> and the concatenation operation form a [[monoid]], the [[free monoid]] generated by Σ.  In addition, the length function defines a [[monoid homomorphism]] from Σ<sup>*</sup> to the non-negative integers (that is, a function <math>L: \Sigma^{*} \mapsto \mathbb{N} \cup \{0\}</math>, such that <math>L(st)=L(s)+L(t)\quad \forall s,t\in\Sigma^*</math>).

A string ''s'' is said to be a ''[[substring]]'' or ''factor'' of ''t'' if there exist (possibly empty) strings ''u'' and ''v'' such that ''t'' = ''usv''.  The [[binary relation|relation]] "is a substring of" defines a [[partial order]] on Σ<sup>*</sup>, the [[least element]] of which is the empty string.