0
$\begingroup$

I came across this sequence when visiting the Longest increasing subsequence problem. In particular, this implementation. I will demonstrate the observation below:

Given

Here we have a sequence of integers:

[0, 1, 1, 2, 1, 2, 2, 3, 1, 3, 2, 5, 2, 3, 7, 6]

Notice from left to right, at each position, the next number is either:

  1. a value already observed
  2. a number larger than the maximum value observed

Thus the following pattern is invalid:

[0, 5, 1, ...]

as the value after 5 must be observed prior or larger than 5.

Question

What is the mathematical term of such a sequence? If no exact term is defined, how might this be formally described? The sequence is not strictly monotonic, but the maximum appears to be monotonically increasing.

$\endgroup$
0
$\begingroup$

I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i \in \mathbb{Z}$ and $a_i \geq a_j$ whenever $i > j$. Of course you could specify bounds on the indices if the sequence it finite. Also it follows from this that the first element is the smallest element.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.