Timeline for Are these finite semirings known?
Current License: CC BY-SA 4.0
30 events
| when toggle format | what | by | license | comment | |
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| S Jan 20 at 18:01 | history | bounty ended | CommunityBot | ||
| S Jan 20 at 18:01 | history | notice removed | CommunityBot | ||
| S Jan 12 at 16:15 | history | bounty started | mathoverflowUser | ||
| S Jan 12 at 16:15 | history | notice added | mathoverflowUser | Draw attention | |
| Dec 17, 2023 at 17:26 | comment | added | mathoverflowUser | related: orges-leka.de/a_class_of_number_theoretic_finite_semirings.pdf | |
| Dec 17, 2023 at 12:50 | history | undeleted | mathoverflowUser | ||
| Dec 17, 2023 at 12:50 | history | deleted | mathoverflowUser | via Vote | |
| Dec 17, 2023 at 10:21 | comment | added | mathoverflowUser | @CommandMaster: Yes, the '$mod$-equations' would prove this, and also I have done some experiments on the computer for small values of $n$. | |
| Dec 17, 2023 at 9:34 | comment | added | Daniel Weber | Do you have any reason to believe this addition is commutative or associative? | |
| Dec 17, 2023 at 8:20 | comment | added | mathoverflowUser | @StevenStadnicki: Is there anything else which I can improve with the question? | |
| Dec 17, 2023 at 8:20 | comment | added | mathoverflowUser | @JoeSilverman: I hope that the question is now more focused and clear. | |
| Dec 17, 2023 at 8:19 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
added explanation about successor graphs and one question about $\oplus,\otimes$.
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| Dec 17, 2023 at 0:52 | comment | added | mathoverflowUser | @JoeSilverman: I have updated the question with the hope that it now becomes more clear. If there is still anything unclear, please do not hesitate to ask. | |
| Dec 17, 2023 at 0:50 | comment | added | mathoverflowUser | @StevenStadnicki: I have updated the question with a table for $\pi_n(N)$ as example. | |
| Dec 17, 2023 at 0:49 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
added table of clarification for pi_n(N)
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| Dec 17, 2023 at 0:12 | comment | added | mathoverflowUser | @StevenStadnicki: To come back to your question about the tree: First the tree is $T_n$ constructed. Then the numbers $N$ which might be bigger thant $n$ are classified based on their smallest prime divisiors recursively on the nodes of the tree. You are right, I have not given the precise definition and it should be proven that those definitions of $\pi_n(N)$ are indeed equivalent. | |
| Dec 17, 2023 at 0:08 | comment | added | mathoverflowUser | @StevenStadnicki: Thanks for the pointer with $D(n)$. It should have been $D(N)$ and yes, the way $\pi_n(N)$ is defined make the properties you mention trivial, which I have also changed. It does not make the quesiton less research-level, because it still is the question about the semirings if it is new or not. | |
| Dec 17, 2023 at 0:06 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
corrected based on suggestion by StevenStadnicki
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| Dec 16, 2023 at 23:15 | comment | added | Steven Stadnicki | I did not downvote, but a few more notes on why you might have gotten downvoted, things that suggest this question is not research-level: (1) your definition of $\pi_n(N)$ has the condition $x\in D(n)\cap[n]$, but trivially $D(n)\subset [n]$, so the intersection isn't needed. (2) Of the conjectured properties of $\pi$ that you mention, the second one is trivial and the first and third are almost trivially false: $\pi_8(7)=4$ and $\pi_5(8)=5$. Perhaps you mean $\pi_n(N)\mid n$? But this is also trivial, since the domain over which the max is taken is just the divisors of $n$. | |
| Dec 16, 2023 at 21:02 | comment | added | mathoverflowUser | @StevenStadnicki Thank you for your comment. I will answer your question tomorrow. | |
| Dec 16, 2023 at 20:14 | comment | added | Steven Stadnicki | I think you might have either a typo or thinko — above the tree you mention querying a number about its smallest prime divisor, but the way you recurse suggests that the key quantity is actually the number's largest prime divisor. You do eventually get to the smallest at the top level by stripping away all the larger ones, but every arrow from one level to the next is actually a multiplication by that largest prime divisor. | |
| Dec 16, 2023 at 17:09 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
removed data
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| Dec 16, 2023 at 17:06 | comment | added | mathoverflowUser | @JoeSilverman: I thought that more examples are better. I will change that. Thanks for your comment. | |
| Dec 16, 2023 at 16:47 | comment | added | Joe Silverman | I wasn't the downvoter, but the downvote might have to do with the fact that you included so many screens of data, which makes it very hard to figure out what's important and what's not. | |
| Dec 16, 2023 at 16:03 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
corrected typo.
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| Dec 16, 2023 at 16:00 | comment | added | mathoverflowUser | I do not understand the downvote. :-( | |
| Dec 16, 2023 at 14:14 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
added more examples.
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| Dec 16, 2023 at 14:10 | history | undeleted | mathoverflowUser | ||
| Dec 16, 2023 at 11:31 | history | deleted | mathoverflowUser | via Vote | |
| Dec 16, 2023 at 10:36 | history | asked | mathoverflowUser | CC BY-SA 4.0 |