Results 1 to 7 of 7
Like Tree1Thanks
  • 1 Post By romsek

Thread: Applications of Recurrence Relations: Ternary string question

  1. #1
    Newbie
    Joined
    Nov 2017
    From
    tornoto
    Posts
    3

    Applications of Recurrence Relations: Ternary string question

    I'm having trouble tackling this problem,

    "Find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0s"

    I was wondering where a good place to start is with questions like these
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,014
    Thanks
    1152

    Re: Applications of Recurrence Relations: Ternary string question

    What do you mean by "ternary string"? Is that a string where every character may be one of three possible values?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2017
    From
    tornoto
    Posts
    3

    Re: Applications of Recurrence Relations: Ternary string question

    Yes it's like a binary string except there can be a 2, so the possible values are 0, 1, 2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,918
    Thanks
    2491

    Re: Applications of Recurrence Relations: Ternary string question

    Thanks from SlipEternal
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,485
    Thanks
    2730
    Awards
    1

    Re: Applications of Recurrence Relations: Ternary string question

    Quote Originally Posted by masonD View Post
    I'm having trouble tackling this problem,
    "Find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0s"
    I was wondering where a good place to start is with questions like these
    As stated this is what we let $\mathcal{T}_n$ be the collection of ternary strings of length $n$ that contain two consecutive 0s".
    We denote the number of elements in $\mathcal{T}_n$ by ${t}_n$.
    $\mathcal{T}_1=\emptyset$ so $t_1=0$
    $\mathcal{T}_2=\{00\}$ so $t_2=1$
    $\mathcal{T}_3=\{~000,~100,~200,001,002\}$ so $t_3=4$

    Be sure that I constructed those correctly & that I counted all.
    How was $\mathcal{T}_3$ constructed using $\mathcal{T}_1,~\&~\mathcal{T}_2~?$

    What does $\mathcal{T}_4$ look like and how is it constructed?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,918
    Thanks
    2491

    Re: Applications of Recurrence Relations: Ternary string question

    Quote Originally Posted by Plato View Post
    As stated this is what we let $\mathcal{T}_n$ be the collection of ternary strings of length $n$ that contain two consecutive 0s".
    We denote the number of elements in $\mathcal{T}_n$ by ${t}_n$.
    $\mathcal{T}_1=\emptyset$ so $t_1=0$
    $\mathcal{T}_2=\{00\}$ so $t_2=1$
    $\mathcal{T}_3=\{~000,~100,~200,001,002\}$ so $t_3=4$

    Be sure that I constructed those correctly & that I counted all.
    How was $\mathcal{T}_3$ constructed using $\mathcal{T}_1,~\&~\mathcal{T}_2~?$

    What does $\mathcal{T}_4$ look like and how is it constructed?
    take another look

    $t_3=5$
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,485
    Thanks
    2730
    Awards
    1

    Re: Applications of Recurrence Relations: Ternary string question

    Quote Originally Posted by romsek View Post
    take another look

    $t_3=5$
    Thank you. I cannot even count to 5!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Dec 8th 2012, 05:04 AM
  2. [SOLVED] Probability question involving recurrence relations
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 5th 2011, 02:07 PM
  3. Simple recurrence relations question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Feb 7th 2011, 12:15 PM
  4. Recurrence of a Ternary Sequence
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Mar 8th 2010, 08:59 PM
  5. Replies: 3
    Last Post: Feb 10th 2009, 04:51 AM

/mathhelpforum @mathhelpforum