Description of an Increasing Maximum Value in a Sequence of Integers

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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.




sequences-and-series




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    up vote
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    down vote

    favorite
    1












    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.




    sequences-and-series




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite
      1









      up vote
      0
      down vote

      favorite
      1






      1





      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.




      sequences-and-series




      share|cite|improve this question











      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.





      sequences-and-series





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      share|cite|improve this question




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      asked Aug 2 at 22:33









      pylang

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          I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i in mathbbZ$ 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.






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            I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i in mathbbZ$ 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.






            share|cite|improve this answer

























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              0
              down vote













              I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i in mathbbZ$ 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.






              share|cite|improve this answer























                up vote
                0
                down vote










                up vote
                0
                down vote









                I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i in mathbbZ$ 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.






                share|cite|improve this answer













                I don't know of any name for it, but you could formally define such a sequence as: $(a_n)$ where $a_i in mathbbZ$ 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.







                share|cite|improve this answer













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                share|cite|improve this answer











                answered Aug 3 at 0:28









                Ken Tjhia

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