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Hi people

In a recent presentation by Sedgewick, he recounts in 1977 Flajolet noticed that they had a formula in common, both in different domains (see slide 4 in http://www.cs.princeton.edu/~rs/talks/AofA2AC.pdf )

I saw the same thing in an article on tantalizing links between matrix eigenvalues distributions, nuclear physics and Riemann's zeta zeros http://web.williams.edu/go/math/sjmiller/public_html/RH/Hayes_spectrum_riemannium.pdf

My question is: Say I have a formula/equation - how would I go about searching for an occurrence of the formula in other domains? Can I make Wolfram Alpha do that?

Thanks for any pointers

Daniel Bilar

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This should be CW –  Igor Rivin Jun 4 '12 at 18:36
    
I am sorry, what is CW? –  Daniel Bilar Jun 4 '12 at 18:50
    
Thanks, I checked the community wiki button –  Daniel Bilar Jun 4 '12 at 19:00
1  
I also found this latexsearch.com "LaTeX Search ... allows researchers to search for LaTeX formatted equations in all of Springer's journals. That's something you can't do with Google, or any other search engine.The ability to connect obscure mathematical discoveries from disparate fields of science could soon be facilitating new avenues of research, perhaps even new methodologies." –  Daniel Bilar Jun 4 '12 at 21:57

2 Answers 2

up vote 6 down vote accepted

If you can turn your formula into an integer sequence, put it into OEIS. This includes:

Plug in integer values for your parameters and enter the outputs.

If your construction produces a sequence of vector spaces, input their dimensions.

If you have a polynomial with integer coefficients, input its coefficients.

If you have a triangular array of integers, enter it by diagonals.

If you have a probability distribution, and its moments are integers, enter those.

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That's clever, David! –  Patricia Hersh Jun 4 '12 at 19:28
    
I'll try this out with a few test cases - thanks David :D –  Daniel Bilar Jun 4 '12 at 20:23

This question is about as easy to answer as: how do I go about proving theorems? Find similarities between seemingly dissimilar things is a big part of what makes a good mathematician. Maybe this will be automated some day, but I hope not.

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There are techniques to guide proofs, see Velleman for example: amazon.com/How-Prove-It-Structured-Approach/dp/0521446635 Beyond intuition, there must be some heuristics out there –  Daniel Bilar Jun 4 '12 at 18:53
    
There are a lot of heuristics, but how helpful they are is an open question (I am not being facetious, I really don't know...) –  Igor Rivin Jun 4 '12 at 19:49
    
There was a long discussion touching on that issue over at Tim Gowers's blog: gowers.wordpress.com/2012/03/21/… –  Daniel m3 Jun 4 '12 at 23:13

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