- #1
Liquid7800
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After studying Generating Functions some, I wondered this question:
1). Take an arbitrary sequence of numbers for example:
{p1,p2,p3,p4...pN} and get/find a Generating Function for that sequence.
2). Now 'remove' an arbitrary sequence members from the above set :{p1,p2,p3,p4...p100} which might look like this after removal of arbitrary sequence members:
{p1,p2,,p8,,,,p20,p21,p22,,,,,,p45,,,...p100}
Now the question becomes:
Can you produce a Function (another Generating Function?) to make the sequence 'recognizable' again...how would you re-generate or re-facilitate the 'missing' sequence members or 'holes'...maybe using some combination of techniques to define a frame of 'reference' from an initial encoding from the original (full) sequence.
I have no idea if this problem(s) has been researched or even solved before...
but I was just thinking of how you could 'create' or 'fill' missing information mathematically...and the problem of sequence reconstruction came to mind.
If I am unclear as to what I am asking please let me know.
...I guess what I am looking for is some starting points, pre-requisite mathematical knowledge, theory, subject areas, refernce materials etc., from people who know what they are doing--- (anyone worked on this kind of thing before?)...
This is going to be a personal thing to mathematically immerse myself in as a project to explore, since I love series and Generating Functions.
Thanks for listening!
1). Take an arbitrary sequence of numbers for example:
{p1,p2,p3,p4...pN} and get/find a Generating Function for that sequence.
2). Now 'remove' an arbitrary sequence members from the above set :{p1,p2,p3,p4...p100} which might look like this after removal of arbitrary sequence members:
{p1,p2,,p8,,,,p20,p21,p22,,,,,,p45,,,...p100}
Now the question becomes:
Can you produce a Function (another Generating Function?) to make the sequence 'recognizable' again...how would you re-generate or re-facilitate the 'missing' sequence members or 'holes'...maybe using some combination of techniques to define a frame of 'reference' from an initial encoding from the original (full) sequence.
I have no idea if this problem(s) has been researched or even solved before...
but I was just thinking of how you could 'create' or 'fill' missing information mathematically...and the problem of sequence reconstruction came to mind.
If I am unclear as to what I am asking please let me know.
...I guess what I am looking for is some starting points, pre-requisite mathematical knowledge, theory, subject areas, refernce materials etc., from people who know what they are doing--- (anyone worked on this kind of thing before?)...
This is going to be a personal thing to mathematically immerse myself in as a project to explore, since I love series and Generating Functions.
Thanks for listening!