bio | website | grpaseman.wordpress.com |
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location | S.F. Bay Area | |
age | ||
visits | member for | 5 years, 6 months |
seen | 2 hours ago | |
stats | profile views | 4,943 |
The sdfae.* websites are not up (technical difficulties); until they rise, I invite you to check out http://grpaseman.wordpress.com for the month of October and your dose of System Design.
Ask Me About System Design. I am willing to do email correspondence on the subject.
Social Networking Data
__Location: (Headed to) Back from Seoul for ICM2014. See MathOverflow @ ICM2014 : We Want You! for detail, including email address
__Interests: General Algebra, Computability, Enumeration, Prime Gaps
__Project: Bounds on Jacobsthal's Function
__Project: Combinatorics of P's Ring Toss
__Have: copy of Erik Westzynthius' (Only?) Paper
__Want: symbolic dynamics on infinite directed sets, esp. forests
__Contact: through Will Jagy, or guess the following Hangman dro_d__r_ard__ma_l.com
(Please do not merge keep me, or even merge me: merge keep 3402 instead)
Jul 28 |
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Recent progress on the busy beaver problem?
The question as it stands implicitly asks for references on a topic in computability theory which could be started in an undergraduate class, but not finished there. It also asks (in an interesting way) for that part of the state of the art where contributions can be made. If amateurs found a way to, say, classify state machines so that some classes are recognizably non halting, that would help in mathematical logic and elsewhere. I am struggling to understand why this question is "off-topic". Gerhard "Please Explain Or Please Reopen" Paseman, 2015.07.28 |
Jul 27 |
answered | Recent progress on the busy beaver problem? |
Jul 27 |
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Counting function for prime pair with bounded gaps between them
Right now there is no polynomial guarantee that such a bound exists. The Hardy-Littlewood conjectures concerning prime k-tuples and associated calculations can tell you how many such are expected to appear (something like $Cx/(\log x)^{2n}$ for an effectively computable C ). If you are willing to take those conjectures into account, you may get what you want. Gerhard "And Hopefully What You Need" Paseman, 2015.07.27 |
Jul 27 |
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Maximal opening angle of a polygon from a point
You need to take care. O(log n) is possible when the list of vertices is already sorted by this orientation, or nearly so. It is not clear to me that the polygon is presented in such a form, nor is it clear that n is small enough not to matter. Gerhard "Without Chaos, Can't Appreciate Order" Paseman, 2015.07.27 |
Jul 27 |
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Computer calculations in a paper
Lest my statement be interpreted too strongly, let me say that I have not personally verified the contents. They may contain errors. However, the thoroughness and clarity of the exposition lead me to the confidence that I can replicate and verify the results, as can anyone else. When I am ready, I will check their work because they wrote down enough for me to do so. Gerhard "Then I'll Build The Bridge" Paseman, 2015.07.26 |
Jul 26 |
answered | Computer calculations in a paper |
Jul 22 |
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Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
Wow @Gerry, thanks for the link! I will peruse the paper more closely, but on first skimming, I don't see any remarks that say the paper's results apply to $\sigma$. I do find a 1991 paper on $\omega$ that looks interesting though. Gerhard "Deeper Into The Rabbit Hole" Paseman, 2015.07.21 |
Jul 21 |
revised |
Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
deleted 1 character in body |
Jul 21 |
answered | Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$? |
Jul 21 |
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Elementary treatment of elementary functions in constructive math
It might be of interest to go through an example you know will work. Can you do this for a linear function? A sum or product of such functions? Gerhard "Found A New Function Class?" Paseman, 2015.07.21 |
Jul 21 |
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Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
@zeraouliarafik , I recommend that you no longer comment on this answer; it is getting too long to follow. Also, you should check that such n do not satisfy your condition: \sigma(114^(114k)) is odd. Further, I do not want to be emailed on conjectural statements. You should show that you put in some work to resolve a question you have. Gerhard "Look At Twice A Square" Paseman, 2015.07.20 |
Jul 19 |
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Dividing the edges and diagonals of a polygon among disjoint sub-polygons
Using a regular n-gon for reference, I find the diagonals closest to the center the most restrictive, suggesting that m will be closer to (perhaps greater than) n than to n/2 for large n. Gerhard "But Geometry Might Help Though" Paseman, 2015.07.19 |
Jul 19 |
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Dividing the edges and diagonals of a polygon among disjoint sub-polygons
I deleted my comment because I thought diagonals were also not to be shared. However, I thought a sub-polygon of a convex polygon was also convex (I guess vertex order matters?). There may still be a design interpretation, but my original one does not quite capture the problem. Gerhard "Thinks This Still Isn't Geometry" Paseman, 2015.07.19 |
Jul 18 |
reviewed | Approve Comparing algebraic group orbits over big and small algebraically closed fields |
Jul 17 |
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A question on integers relatively prime to their Euler totien function
It might clarify things to note that this is "happening inside S", where S is the set of squarefree numbers and has a natural semilattice structure on it. Z is just X intersect the complement of a join-ideal of S generated by those members of Y that are not primes. If there are finitely many nonprime members of Y, it may be straightforward to show the ideal grows slowly. It may also be possible to find a "sparse infinite cover" which would force Z to be much smaller than you hope. Gerhard "This Mindset Worked Once Before" Paseman, 2015.07.17 |
Jul 17 |
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Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
I recommend further discussion in email, not comments. Also, it is unclear how the paper relates to the problem. Iterates of the totient function are not necessarily related to iterates of the sigma function. Gerhard "You Can Explain In Email" Paseman, 2015.07.16 |
Jul 16 |
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Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
I think you should not accept this version. I am thinking about a proof, as well as related questions (which you should think about as well). If there is no further progress, I will add a further edit which says what difficulties there are in showing that such a sequence exists. If you find the result acceptable, it would be OK with me to accept that future version. Gerhard "Now Back To The Present" Paseman, 2015.07.16 |
Jul 16 |
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Which classes of functions are “convolution ideals”?
Ah yes. I was not paying enough attention. Ideal would be appropriate, although I might still prefer "absorbing set". However, the literature I know talks only about things like left-absorbing elements b (ab=b). Gerhard "Seeks Something Even More General" Paseman, 2015.07.16 |
Jul 16 |
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Which classes of functions are “convolution ideals”?
I prefer "closed under convolution". If the set of functions combined with convolution were an algebra (commutative semigroup?), you would be looking for the subalgebras of this universal algebra. Gerhard "Do You Seek This Generality?" Paseman, 2015.07.16 |
Jul 16 |
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Is there a fixed integer $x>1$ satisfing ${\sigma}^{k}(x)\equiv 0\pmod{x}$ for all positive integers $k$?
@zeraouliarafik: please delete your last comment. I present my personal information the way I do to keep a low profile. Gerhard "Doesn't Need Spambots Knowing It" Paseman, 2015.07.15 |