I am currently trying to solve a problem which has already been posted once here: Compute the Hilbert-Samuel function

However the above link does not have any answers or comments at all, and I am far from sure if what I have worked out is correct. Thus, I would have liked to post the question myself. I'm new to this website, and I'm not sure if one is allowed to post the same problem again as a separate question. I would be very grateful if someone would advise me what to do in this situation.

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    $\begingroup$ You can post the same question as a new question : link to it or perhaps later ask for a merge. What you need as context is not necessarily what you have tried , unless you want feedback on your attempt. See if you can locate sources for the question (perhaps something on computing Hilbert-Samuel functions) , see if you can find similar computations (Theorems or results that show that some ideal is an ideal of finite co-length) and you can put these in as well. You may attempt to post a question and then you can post it here for feedback and ping me. I'm not familiar with the subject, but... $\endgroup$ Jun 30, 2021 at 5:02
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    $\begingroup$ ... all said and done I kind of feel like adding some things that might interest a person slightly below that level (since I have been far into the subject but not this far!) will give you a lot of weightage. You can also tag [solution-verification] , but that's only IF you want verification of a solution you have written (and not specifically an answer to the question). If you post the same question as in that post verbatim, I'm afraid it may not hold up : so I'm just ensuring whenever it's up that it's got the best chance of being received and appreciated by anyone on site. $\endgroup$ Jun 30, 2021 at 5:04
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    $\begingroup$ This is the Wiki link for HS functions , This is another link. I couldn't find any sources where computation is explicitly performed (except for some theorems), but if you have sources for this you can put these in as well. Including these links (along with maybe one line about each link, only if necessary) will be super-beneficial. Your question will do well. $\endgroup$ Jun 30, 2021 at 5:14
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    $\begingroup$ @TeresaLisbon Thanks a lot for you help! I have posted the question here math.stackexchange.com/questions/4186713/… $\endgroup$
    – user940160
    Jun 30, 2021 at 7:01
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    $\begingroup$ Your question is very good, as I see it. You have a source, an attempt that seems to have worked one part out, and everything is neatly stated. I hope your question is well received and gets a good answer. If anybody asks you to modify the question in some way so that it looks better, you can follow their suggestions. Very happy to have been of some assistance to you. $\endgroup$ Jun 30, 2021 at 7:15
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    $\begingroup$ @TeresaLisbon Thanks once again! $\endgroup$
    – user940160
    Jun 30, 2021 at 7:16
  • $\begingroup$ @TeresaLisbon I feel that you can convert your comments together into one answer and write it and then user940160 can accept it. $\endgroup$
    – user876009
    Jun 30, 2021 at 10:20
  • $\begingroup$ @user940160 I don't have an answer to the main question : OH I see , this one! Ah, well, I could do it. I'll probably do it. $\endgroup$ Jun 30, 2021 at 10:36

1 Answer 1


So the question is up and running here. It has two up votes and 20 views as of the time of writing (and 5 up votes and 51 views after some more time), and seems to be good!

Criterion that I requested for fulfillment from the new question, which were heeded, include :

  • The source, which was specified. It was found by the OP.

  • A reference to the old question.

  • A complete attempt for one part of the question, along with a partial attempt for the second part.

In addition, I have linked for the purposes of the OP and others' understanding, some posts above regarding the definition and some theorems about the HS function. These are here and here. The OP may feel free to use these documents to further the context of the question if necessary, or if prompted in the comments.

Either way, I thank the OP for their efforts to get the question running, and I hope it will receive an excellent answer and further improve the quality of the site, given that there hasn't been too much discussion on HS functions on the site.


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