Is there are name for the number series which has the following pattern

Starts small, rises in the middle and goes down as in


To give you a background of why this question came up. I am relearning sorting algorithms and there was one case on quick sort (sorting is based on divide and conquer and the numbers lesser than the pivot goes to the left and the numbers greater than the pivot goes to the right) where if we chose the pivot as the median in every single slice, we get quadratic performance.

So, if the sequence is something like


and during each iteration, if the pivot is exactly the median, then in case of 1,4,2 in the second iteration, the left side is 1,2 and right side is empty. Finally the pivot is appended left side before the right side. If, throughout the entire bag of numbers, the left/right side is empty, then we suffer quadratic performance.

I am trying to blog about this and I am unable to give this series any name. Felt that I should leave it to the math experts.

Tried Googling and searching within the stackexchange but couldn't find (probably didnt know what to search for)

  • $\begingroup$ A mildly related fact: if a sequence "reads exactly the same forwards as backwards" it is called palindromic. But that's not what you are asking about. $\endgroup$ – André Nicolas Aug 10 '12 at 6:40
  • $\begingroup$ Thanks Andre. Edited the question to provide more details. $\endgroup$ – Arun Manivannan Aug 10 '12 at 6:51
  • $\begingroup$ Unimodal sequence $\endgroup$ – Quixotic Aug 10 '12 at 7:02

It could be called "unimodal".

  • $\begingroup$ Great !!! Thanks Robert. (Sorry, cant vote the answer up with my sad reputation numbers) $\endgroup$ – Arun Manivannan Aug 10 '12 at 7:10

Maybe here? http://www.mathematische-basteleien.de/palindromes.html

  • $\begingroup$ This doesn't seem to be what the question is asking about. $\endgroup$ – Nate Eldredge Aug 10 '12 at 12:49

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