Solution 64: Dyck Path Pattern Avoidance (UDUDUD) and Containment

  • Published on Nov 1, 2018
  • Let's avoid paths with UDUDUD, while making sure that they contain DU at the center.
    Congratulations to Vishaal Ram, reynolds45, Minh Cong Nguyen, enisheadpay, Kevin Tong, Bigg Barbarian, Rishav Gupta, Nicola C, and Czeckie for successfully solving the last week's math challenge question! Vishaal Ram was the first person to solve the question.
    Your support is truly a huge encouragement.
    Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos!
    Every subscriber and every like are wholeheartedly appreciated.
    Welcome, everyone! My channel hosts one weekly math challenge question per week (made by either myself, my family, or my friends), which will be posted every Wednesday. Please comment your proposed answer and explanation below! If you are among the first ten people with the correct answer, you will be recognized in the next math challenge video. The solution to this question and new question will be posted next Wednesday.
    For more Weekly Math Challenges:

Comments • 11

  • Pete Berg
    Pete Berg 5 months ago

    Wait, why an= floor (n/2) ?

    • Pete Berg
      Pete Berg 5 months ago

      Are we comparing the number of up in the left and and the possibilites of the mid way?
      Because the midway determines the possibilities for that an

  • Kyro
    Kyro 7 months ago

  • δτ
    δτ 7 months ago

    What if only UDUD...DU...UD is omitted as a trivial Dyck path for each n?

  • JackTheSpades
    JackTheSpades 7 months ago +2

    Wait, so something like U-DUU-DU-DDU-D is not valid then?
    I thought the 'avoid UDUDUD' was referring to consecutive use.

    • JackTheSpades
      JackTheSpades 7 months ago

      @LetsSolveMathProblems That's fair. I was wondering why the subset thing was mentioned but seeing this it makes more sense now.

    • LetsSolveMathProblems
      LetsSolveMathProblems  7 months ago +1

      Pattern containment/avoidance deals with whether we have a certain subsequence as part of the original sequence. A subsequence, by definition, does not have to be consecutive terms of the sequence. I hoped to implicitly clarify this in the problem statement (Note that the example I provided at 1:19 shows that a non-consecutive pattern must work as well because UUDUDD does not consecutively contain UUDD).

  • indomit
    indomit 7 months ago +3

    it's 080 actually :)

  • Zain Majumder
    Zain Majumder 7 months ago +1

    Is Dyck path the official name? I think "mountain path" is a good descriptor.

    • 佐藤裕也
      佐藤裕也 7 months ago +1

      I googled and found this article;
      The pictures of the article are basically the same as this video except 135 degrees rotated.