1.6: Sorting- Part 0

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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.

Practice

Checkpoint \(\PageIndex{1}\) Write all the permutations of the string “mat”. List them in lexicographic order.

Checkpoint \(\PageIndex{2}\) The lexicographic order is just one of the orders. How many possible orders of the permutations of the string “mat” exist?

Checkpoint \(\PageIndex{3}\) How many possible orders of the permutations of the string “math” exist?

Checkpoint \(\PageIndex{4}\) As the length of the string increases, how much does the number of possible orders increase?