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Ask Me About System Design. I am willing to do email correspondence on the subject.

Social Networking Data

__Location: Headed to 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)


2d
awarded  Nice Answer
Jul
22
comment Magic squares with specific properties
@Robert, What happens if you subtract 43 from each of the entries of your latest example? Gerhard "Hoping The Remainders Are Small" Paseman, 2014.07.22
Jul
22
comment Removing an article from arxiv
Try a different journal, or rewrite the paper. The policy of ArXiv is to keep all versions. You can withdraw a paper (see the ArXiv instructions), but the previous versions will still remain. Gerhard "Like The Bell Already Rung" Paseman, 2014.07.22
Jul
21
comment a book comparable to Development of mathematics in the 19th century by F.Klein?
This forum is not the best one for your question. A new forum for mathematics educators is on stackexchange, you might ask there. If you focused on one book, and made it clear what substantive efforts you took to find it that did not work, and it was within the scope of this forum, you might find the modified question released from hold and perhaps receiving a satisfactory answer. Right now, "Books that V. Arnold liked" is not quite right for this forum. Gerhard "Other Titles Might Be Accepted" Paseman, 2014.07.21
Jul
19
comment For $x,y\ge 2$ does $x^4+x^2y^2+y^4$ ever divide $x^4y^4+x^2y^2+1$?
Taking that particular example, one gets that the desired divisibility implies -2400(49y^2+2402) is divisible by the "smaller" quartic. Since the factor is odd, this reduces to 3*5^2(49y^2+2402), which quickly limits the size of feasible y. Perhaps one can show quickly this way that x cannot be small. Gerhard "For All But Infinitely Many" Paseman, 2014.07.19
Jul
19
comment For $x,y\ge 2$ does $x^4+x^2y^2+y^4$ ever divide $x^4y^4+x^2y^2+1$?
Suppose one considers specific instances for x, e.g. 2401 + 49y^2 + y^4 divides (or not) 2401y^4 + 49y^2 +1. Can one come up with nice conditions on y to predict when this happens? Can such conditions be "uniformized" over families of x? Gerhard "Likes Solving By Plugging In" Paseman, 2014.07.19
Jul
19
comment Is the Manickam-Miklós-Singhi Conjecture solved?
I think a more neutral and direct answer would be along the lines of "yes, I have read the paper", or "no, I haven't", or "I talked to someone who said she had read the paper". Although I appreciate the background in your post, it does not address what I think the real question is: "Does anyone know of any independent verification or refutation of (ideas in) paper X?". Then those who have such information can decide to share that here on MathOverflow (with opinions or statements about the correctness taken elsewhere, not here), or not. Gerhard "Doesn't Know Who Read It" Paseman, 2014.07.19
Jul
15
comment A problem in symbolic dynamics
To be clear, I think there are sets X_n for which your desired condition will not hold because the sets X_n will avoid mth powers for sufficiently large m. However, the obvious thing to try (take jth character to avoid symbol a[j]) does not make it clear that one can avoid mth powers. Gerhard "Ask Me About Powerful Strings" Paseman, 2014.07.15
Jul
15
comment A problem in symbolic dynamics
If y is a fixed word of length k, and you are only looking at subwords of length n of y^n, you will have at most k distinct subwords. Thus, for large n, the challenge will not be finding a linear growth function. It will be finding a y that "threads" through all the sets X_n. If I am careful, I think I can find m such that no mth power will be a substring of any member of any X_n. Gerhard "Guesses The Answer Is 'No'" Paseman, 2014.07.15
Jul
15
comment Are there isomeasure simplices?
If you mean, for a given tuple of base, volume, edge sum and area sum, yes, there will be finitely many. There will be uncountably many classes of such isomeasure objects, even if you fix volume and (say) sum of edge lengths. Gerhard "Hopes He Got It Right" Paseman, 2014.07.14
Jul
15
comment Are there isomeasure simplices?
I think generically there will be more. Fix the base triangle B, a height h, and a normal direction. Points in a plane at height h from B determine a fixed volume, and that plane is divided into many smooth compact level sets, each set corresponding to a constant sum of edge lengths. For each nontrivial level set, there are often for uncountably many values of the sum of areas at least two and perhaps more points on the level set which share that value for sum of areas. I think you get uncountably many which aren't congruent. Gerhard "Ask Me About Twisty Thinking" Paseman, 2014.07.14.
Jul
14
comment Are there isomeasure simplices?
Now that this question has appeared, I can add my second comment: fix some scalene triangle and sum of edge lengths L, and consider the compact figure of all points (x,y,z) such that the suggested simplex has sum of edge lengths L. Now to each such point, associate the sum of areas and volume. There will be many cases when two points on the figure have the same ordered pair (a,v): the trick is to find those when v is nonzero. Fixing a v, one finds level curves on the surface at the same height with constant volume. Now, ... Gerhard "Leaves The Rest To You" Paseman, 2014.07.13
Jul
13
comment What kind of algebra is the class of ordered pairs equipped with the binary operation which forms them?
It depends on how you arrange things. The Jonsson-Tarski algebras mentioned in another answer have a nice equational setup: l(p(x,y))=x=r(p(y,x))= p(l(x),r(x)). This gives trivial or infinite algebras, and is a nice example to use in studying algebras with pairing and projection functions. Gerhard "Ask Me About System Design" Paseman, 2014.07.13
Jul
13
comment Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
I also suspect that such algebras will yield a normal form, or provide a small "unnormalizable" core. You might look at Knuth-Bendix to see if someone has come to a similar conclusion. Gerhard "Or Tweak The Relational Properties" Paseman, 2014.07.13
Jul
13
comment Which algebraic theories have the property that $\mid$ is antisymmetric for all free algebras?
In model theory, one has some notion (algebraic with respect to parameters a) that is related to this. I don't know if there is a standard name for the preorder. For finite algebras, there is a classification of such algebras for which (I suspect) the relation is total. You might find Hobby and McKenzie's text on tame congruence theory of interest, especially the foundational part. Your notion can be extended by replacing = by an arbitrary congruence of X, and may have been considered for finite X by Hobby and McKenzie. Gerhard "Doing This With Fuzzy Memory" Paseman, 2014.07.13
Jul
13
comment Reading Papers in a Language you don't Speak
You can also look for French language fora (perhaps on Stackexchange), and ask for help. Best to build up a few related questions before asking. Also, you can try searching for those phrases appearing elsewhere, and see if the translation works on those documents you find. In some places you can find a helpful person who can speed up the translation process (perhaps another student who did the work already). Gerhard "Had To Use Paper Dictionary" Paseman, 2014.07.12
Jul
13
comment Reading Papers in a Language you don't Speak
Struggle. Gerhard "Did It. You Can Too" Paseman, 2014.07.12
Jul
10
answered Do's and don'ts of writing survey papers
Jul
9
comment maximum sum of angles between $n$ lines
Also for d=2, n=3 rays, there are other optimal configurations, including all angles being 2pi/3. Gerhard "Is Not Always Right Thinking" Paseman, 2014.07.09
Jul
9
comment maximum sum of angles between $n$ lines
In the plane containing two lines, there are usually two choices for angle. Do you want the larger choice or the smaller? If the former, use the same line n times for pi times (n choose 2) radians. If the latter, for n<=d go orthogonal and multiply the previous estimate by 1/2. Gerhard "Happy To Do Easy Cases" Paseman, 2014.07.09