Timeline for How to invert the matrix [n choose 2j - i] ?
Current License: CC BY-SA 3.0
10 events
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| Oct 31, 2011 at 4:18 | comment | added | Mike Spivey | @Leonid: My apologies for responding so late to your question; somehow I didn't get pinged by your use of "@Mike." All of the matrices in our paper are lower triangular, so the methods may not directly apply. However, one of the core ideas is that elementary and complete symmetric polynomials are inverse to each other, in some sense, and maybe you can adapt that idea to your situation. See, for example, p. 296 of Richard Stanley's Enumerative Combinatorics, Vol. II. | |
| Jun 28, 2011 at 11:15 | history | edited | Emmanuel Briand | CC BY-SA 3.0 |
typo corrected
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| Jun 28, 2011 at 10:44 | history | edited | Emmanuel Briand | CC BY-SA 3.0 |
Added references and explanations for the evaluation of a Schur function.
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| Jun 28, 2011 at 0:47 | vote | accept | Leonid Petrov | ||
| Jun 28, 2011 at 0:47 | comment | added | Leonid Petrov | @Mike: Many thanks for the link! So I have managed to write the inverse in terms of the skew Schur functions as is suggested in the answer. Does your paper give any other, better way of writing the inverse? | |
| Jun 27, 2011 at 19:57 | comment | added | Mike Spivey | @Igor: Full text is available via my web site here: math.pugetsound.edu/~mspivey/Symmetric.pdf. | |
| Jun 27, 2011 at 6:12 | comment | added | Leonid Petrov | Thank you very much for this idea, I think it could really lead to something. | |
| Jun 27, 2011 at 1:56 | comment | added | Igor Rivin | There is more on this sort of thing in: Symmetric Polynomials, Pascal Matrices, and Stirling Matrices Michael Z. Spivey1, Andrew M. Zimmer (full text seems to be readily available). | |
| Jun 26, 2011 at 22:31 | history | edited | Emmanuel Briand | CC BY-SA 3.0 |
edited body
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| Jun 26, 2011 at 21:52 | history | answered | Emmanuel Briand | CC BY-SA 3.0 |