Timeline for Cayley Graphs of Z/nZ with invertible adjacency matrices
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2012 at 12:15 | comment | added | Benjamin Steinberg | I may ask a reformulation. I am actually interested in how badly bad sets can behave in a sense I will try to make precise in the next question when I have free time. Thanks again Will for your feedback. | |
| Jun 7, 2012 at 1:45 | answer | added | Will Sawin | timeline score: 2 | |
| Jun 7, 2012 at 1:36 | comment | added | Will Sawin | I found a new tricky example: $x^2-x+1$ divides $1+x^2+x^3+x^4+x^6$, so $(0,2,3,4,6)$ is a bad set for $n=12$. | |
| Jun 6, 2012 at 23:31 | comment | added | Benjamin Steinberg | I forgot to mention in the question sets of coset representatatives of a proper subgroup. | |
| Jun 6, 2012 at 23:28 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
added 2 characters in body
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| Jun 6, 2012 at 23:27 | comment | added | Benjamin Steinberg | Sorry, I spoke to quickly. I should read comments more carefully. | |
| Jun 6, 2012 at 22:42 | comment | added | Will Sawin | Do they? $x+1$ divides $x^n-1$ for $n$ even. i don't see how that comes from proper subgroups and unambiguous sums. | |
| Jun 6, 2012 at 21:44 | comment | added | Benjamin Steinberg | Characterizing bad is really what I want. I think all the bad examples you mention one from unambiguous sums and subgroups. | |
| Jun 6, 2012 at 20:27 | comment | added | Will Sawin | Or more generally, any set where each residue class mod $b$ that has the same residue mod $a$ has the same number of elements, for $a|b|n$ and $a<b$, This characterization is complete for all prime powers and $n=6$. | |
| Jun 6, 2012 at 20:18 | comment | added | Will Sawin | I think it is more likely that there is a characterization of all bad subsets of $G$, because a random element of this sort of ring is invertible, so you might expect a random subset to be good with high probability. For instance one can construct bad subsets by choosing the same number of elements from each residue class mod $p$, with $p$ dividing $n$, or by taking a union of cosets of a nontrivial proper subgroup. | |
| Jun 6, 2012 at 16:27 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
Format of title
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| Jun 6, 2012 at 15:09 | history | asked | Benjamin Steinberg | CC BY-SA 3.0 |