Timeline for Set of permanents over binary square matrices
Current License: CC BY-SA 3.0
16 events
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| May 17, 2012 at 4:13 | comment | added | user6976 | @Noam: I also did not mention that permanents of these matrices are non-negative. I tend not to mention trivial things in MO answers. | |
| May 17, 2012 at 2:33 | comment | added | Noam D. Elkies | Whether or not $0$ is conventionally included among the "natural numbers", it's not covered by your construction. Well, you might allow $n=0$ and argue that a $0 \times 0$ matrix has zero permanent even though its determinant is $1$. But there's no need for that because for any $n>0$ the zero $n\times n$ matrix has zero permanent. | |
| May 14, 2012 at 22:55 | comment | added | user6976 | In fact the matter is even more complicated: en.wikipedia.org/wiki/Natural_number | |
| May 14, 2012 at 3:04 | comment | added | user6976 | @Noam: In some countries the list of natural numbers starts with 0 (I was very surprised to find it out when I first taught "Introduction to number theory" in the US). | |
| May 14, 2012 at 2:58 | comment | added | Noam D. Elkies | Well, all whole numbers (clearly the permanent may vanish, and it can surely not be negative). | |
| May 13, 2012 at 22:55 | history | edited | user6976 | CC BY-SA 3.0 |
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| May 13, 2012 at 5:45 | comment | added | Gerhard Paseman | I like the example of the matrix with permanent value of n. Another calculation breaks it into the permanent of the order n-1 version and another which is easily calculated to have value 1. Gerhard "Ask Me About System Design" Paseman, 2012.05.12 | |
| May 13, 2012 at 4:15 | comment | added | user6976 | Sequence $l(n)$ is A089477 in the Encyclopedia. | |
| May 13, 2012 at 3:10 | comment | added | user6976 | or the function $l(n)$ which is the smallest number which is NOT a permanent of a $n\times n$-matrix. | |
| May 13, 2012 at 3:01 | comment | added | user6976 | @Mariano: certainly. For example it would be interesting, I think, to understand the function $n(k)$ - the minimal size of a matrix with permanent $k$. I only showed that $n(k)\le k$ but it may be much smaller than $k$. | |
| May 13, 2012 at 2:47 | comment | added | Gerhard Paseman | Will Orrick has enhanced his his maxdet.indiana.edu site to contain information on the determinant spectrum problem as well as maximum determinant for order n 0-1 matrices. Perhaps he can be encouraged to add permanent spectrum info as well. Gerhard "Ask Me About Binary Matrices" Paseman, 2012.05.12 | |
| May 13, 2012 at 2:46 | comment | added | Mariano Suárez-Álvarez | I guess describing the set of permanents for matrices of a specific size could be more involved? | |
| May 13, 2012 at 1:07 | history | edited | user6976 | CC BY-SA 3.0 |
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| May 13, 2012 at 1:04 | vote | accept | Kevin Lawler | ||
| May 13, 2012 at 0:52 | history | edited | user6976 | CC BY-SA 3.0 |
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| May 13, 2012 at 0:45 | history | answered | user6976 | CC BY-SA 3.0 |