Skip to main content
Contents
Dark Mode Prev Up Next
\(\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Pow}{\mathcal{P}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Section 1.6 Sorting: Part 0
If an alphabet has an order, then the strings can be ordered. This is called
lexicographic ordering. For words from a language we often call this alphabetical ordering. Because the order on the strings is determined by the order on the alphabet, we call the ordering
induced .
Subsection 1.6.1 Practice
Checkpoint 1.6.1 .
Write all the permutations of the string βmatβ. List them in lexicographic order.
Checkpoint 1.6.2 .
The lexicographic order is just one of the orders. How many possible orders of the permutations of the string βmatβ exist?
Checkpoint 1.6.3 .
How many possible orders of the permutations of the string βmathβ exist?
Checkpoint 1.6.4 .
As the length of the string increases, how much does the number of possible orders increase?