Timeline for Possible values of the determinant for matrices with elements $\{1, 0, -1\}$
Current License: CC BY-SA 4.0
5 events
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| Apr 21, 2022 at 2:02 | comment | added | rikhavshah | I believe far more determinants are possible, but I'm not aware of any constructions. In particular, Tao and Vu in this paper prove $|det(M)|\in[\sqrt{n!}\,2^{-n^{0.51}},\sqrt{n!}\,n^{1.1}]$ with high probability for M with random $\pm1$ entries. I would therefore guess that there at least $\sqrt{n!}\sim 2^{O(n\log n/2)}$ possible values of the det. | |
| Apr 20, 2022 at 13:52 | comment | added | Martin Rubey | Brute force checking shows that the possible (absolute values of) determinants of $4\times 4$ matrices additionally include 9, 10, 12 and 16. Perhaps with Andrea Marino's answer one can do much more. | |
| Apr 20, 2022 at 10:13 | comment | added | Timothy Chow | Very nice. It reminds me of a construction by Kim, Lee, and Seol that I mentioned in another MO answer, although they were considering permanents rather than determinants. | |
| S Apr 19, 2022 at 23:11 | review | First answers | |||
| Apr 19, 2022 at 23:36 | |||||
| S Apr 19, 2022 at 23:11 | history | answered | rikhavshah | CC BY-SA 4.0 |