16.4.2. Categories of Ternary Strings

Try these first

1. 1.

   What is a ternary string?

   Hint

   Think about the number of different characters involved.

2. 2.

   What does 'strictly increasing sequence' mean?

   Hint

   Consider how each term compares to its predecessor.

3. 3.

   What is a ternary string?

   • A string of two elements
   • A string of three elements
   • A string of four elements

   Hint

   Think about the prefix 'ternary' which suggests three.

4. 4.

   True or False: A sequence can be called strictly increasing if the same number appears twice.

   • True
   • False

   Hint

   Consider the definition of 'strict'.

5. 5.

   Construct the first five valid ternary strings of length 3 and derive T(3).

   Hint

   Focus on ensuring the sequences increase with each character.

6. 6.

   Prove that if T(n) is defined as above, T(5) is double T(4).

   Hint

   Use the established relationship we've discussed.