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

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  • Published on Nov 1, 2018
  • Let's avoid paths with UDUDUD, while making sure that they contain DU at the center.
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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

    usclip.net/video/4Xp4F1h0YZM/video.html

  • 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; mathworld.wolfram.com/DyckPath.html.
      The pictures of the article are basically the same as this video except 135 degrees rotated.