bio | website | grpaseman.wordpress.com |
---|---|---|
location | S.F. Bay Area | |
age | ||
visits | member for | 5 years, 7 months |
seen | Aug 10 at 6:51 | |
stats | profile views | 5,005 |
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)
Aug
10 |
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How distributive are the bad Laver tables?
If one were able to nearly cover a large S_m by embeddings of a smaller S_{2^n}, that would help give you some idea as to how distributive S_m can be. Even knowing how S_2 embeds in S_5 might help in figuring out f(n) in general. Gerhard "Also Look At Their Clones" Paseman, 2015.08.09 |
Aug
9 |
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Diameter of the modified bubble-sort graph
You might be able to show by induction that the permutation (1,n/2)(2,n/2+1)...(n/2-1,n) or something similar is at near maximal distance in the graph from the identity. Even if not, constructing parts of the graph for n up to 5 should give some more clues. Gerhard "Examine The Output More Closely" Paseman, 2015.08.08 |
Aug
9 |
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How distributive are the bad Laver tables?
Are these algebras rigid? Primal? Can you "nearly" embed S_n into a larger S_m ? What literature on Laver tables have you not read yet? Gerhard "Always More Questions Than Answers" Paseman, 2015.08.08 |
Aug
4 |
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Proofs needed for observations regarding prime-partitionable numbers
Actually, we need to make exceptions in the assumption for p=2 (so k=1) and p=3 (so k=2). However, for larger primes p, small even values of k seem to work. Gerhard "Except For Finitely Many Exceptions" Paseman, 2015.08.03 |
Aug
4 |
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A particularly “natural” algebraic structure with three commutative, pairwise-distributive operations
I don't know that you have anything more special than two bilinear operators (convolutions) over (the countable power of) a group. If you have some equational relations involving the two convolutions, you might be looking at something special which has been studied before. There are forms (cf. Movsisyan) of "hyperdistributivity", where certain distributive relations are presumed to hold, but your convolutions may not fit that. Gerhard "Consider The Free Such Algebra?" Paseman, 2015.08.03 |
Aug
3 |
answered | Proofs needed for observations regarding prime-partitionable numbers |
Aug
2 |
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Forbidden coin flips
Just to be clear, you should affirm or deny something like the following: Each coin in the bag is two-sided (one side heads, the other not heads) and each coin d is weighted with probability p_d landing heads up after a flip. Then you can later tie p_d to D(p) as needed. Gerhard "Unless There's Something More Clear" Paseman, 2015.08.02 |
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 |