1,750 reputation
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bio website grpaseman.wordpress.com
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visits member for 5 years, 3 months
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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)


1d
comment Can someone help me with a Towers of Hanoi problem?
Try math.stackexchange.com or their computer science forum. This forum (MathOverflow) is the wrong one for your question. There are also other Internet sources which may help. Gerhard "Look For Java Based Simulations" Paseman, 2015.04.24
Apr
19
comment Repeated random two-steps in $\mathbb{R}^3$: unbounded?
@Arupinski: rename your MathOverflow bookmark to point to Joseph's user page. Gerhard "Saves A Lot Of Time" Paseman, 2015.04.19
Apr
19
comment Primes isolated by large gaps to either side
It would seem that what is known falls short of $p_{n+1} - p_n \gt \log p_n(\log(\log p_n))^k$ being true for fixed $k \geq 1$ and infinitely many $n$. (I think that) Joseph and I would appreciate if you can confirm/deny this assertion, especially the $k \geq 1$ part. Gerhard "Lost In Number Theory Lumberyard" Paseman, 2015.04.19
Apr
19
comment Primes isolated by large gaps to either side
After some minimal checking, I got some of the bases wrong. As far as I know, not even logp_n(loglog p_n)^k is known to occur for infinitely many n and $k > 1$. I will update when I get the numbers straightened out. Maier, Pomerance, Pintz, Tao, Green, Ford, Kolyvagin, and Maynard are still some of the names to check. Gerhard "Or Use A Phone Book" Paseman, 2015.04.18
Apr
19
comment Primes isolated by large gaps to either side
You have results of Maier and Pomerance which say there are (on average maybe?) infinitely many for some real values of $k$ larger than 1. My current investigations and various conjectures suggest your question has the answer yes only for $k$ less than 2. As a start, try Helmut Maier's Chains of large gaps between consecutive primes, done in 1981. Terry Tao announced joint work with four other authors on large gaps, available on ArXiv 1412, with (I think) an upcoming improvement on Maier's result in a followup article. Gerhard "Hope I Got Bases Right" Paseman, 2015.04.18
Apr
17
comment Continuous bijections vs. Homeomorphisms
Thanks for your response. Also, to make the notification system work, use @Gerhard instead of @ Gerhard (@Will in my case). Gerhard "Better Than Firing At Brian" Paseman, 2015.04.17
Apr
17
comment Continuous bijections vs. Homeomorphisms
Wow! In spite of my comments above, I never thought of investigating the lattice of topologies of X itself. Is there any reference investigating the notion of equivalence relations on the lattice of topologies which pertain to being bijectively related? More importantly (for my universal algebraic background) are there important lattice congruences (equivalence relations preserving finite meets and joins) that one could use to help investigate this? Gerhard "Lattices Turn My Mind Inside-Out" Paseman, 2015.04.17
Apr
17
comment Biggest parallelogram inside the union of two translated parallelograms
It convinces me that a maximal solution will be a parallelogram with no sides parallel to the original, and that it is a matter of computing the area when the line through R induces such a parallelogram. This area should vary as a simple quadratic in the x-intercept of the line through R, whose maximum is easily determined. Gerhard "Still Working On The Details" Paseman, 2015.04.17
Apr
17
comment Biggest parallelogram inside the union of two translated parallelograms
Your illustration suggests to me a simple linear program which probably can be made simpler. Consider the intersection U of the two parallelograms, and look at the point of U closest to the letter P in your diagram; call this point R. A line drawn through R at various angles will form the side of an inscribed centrally symmetric parallelogram, and you can compare its area with one of the two answers with sides parallel to the original parallelograms: it will always be larger and will increase until it meets a corner. Gerhard "Stay Tuned For Part II" Paseman, 2015.04.17
Apr
16
comment An upper bound for the length of the continued fraction expansion of $\sqrt d$
What can you say about numbers $d$ where $l$ is 1 or 2? Is it conceivable that the upper bound is constant? Gerhard "If You Dream, Dream Big" Paseman, 2015.04.16
Apr
14
comment 3-colorings of the unit distance graph of $\Bbb R^3$
The above can be improved, since what you care about are the triangle vertices being rainbow and not the edges. However, I think it is best if you leave Gamma out of the picture and talk instead about forbidden rainbow configurations of points. Gerhard "Simplify, But Not Too Much" Paseman, 2015.04.14
Apr
14
comment 3-colorings of the unit distance graph of $\Bbb R^3$
In spite of your efforts, it is not clear what you ask of the coloring. My wording: Given R^3, A,B,C,D on a rhombus as stated, and start a three coloring with the assigned colors to the four points, can the coloring be extended to all of R^3 so that no unit equilateral triangle is rainbow? In particular, we need at least three circles around three edges to receive only two colors. I think this formulation avoiding Gamma is clear, since you are not asking for a proper graph coloring (neighboring vertices get different colors). Gerhard "Gamma Free For More Clarity" Paseman, 2015.04.14
Apr
14
comment Number of ways you can form pairs with a group of people when certain people cannot be paired with each other
The general problem is hard; this specific problem not so much. Since there are 105 ways (you missed a factor of 8), you can almost by hand enumerate the other possibilities. One observation you can make is that there will be two pairs in the first group which will not meet in the second grouping. This should help you compute the total number for the second grouping. Also, this is the wrong forum for your question. Gerhard "Ask Me About Simply Grouping" Paseman, 2015.04.14
Apr
14
revised pseudovarieties and profinite group : do * and g() commute?
I hate gorup and insufficient capitalization
Apr
14
suggested approved edit on pseudovarieties and profinite group : do * and g() commute?
Apr
13
comment Universal anti-Horn classes?
I'm going to spout some moderately informed nonsense, with the hope that some sense and a possible answer you need can be found in it. Such classes can be imagined as unions or coproducts of varieties, which is like saying a set is a union of its elements. If there is a uniform description to these elements, there may be more interest; otherwise, do you care about my laundry list and should I care about yours? Coproducts should be better understood, but that may mean doing a lot of laundry. Gerhard "Read This Metaphorically, Not Literally" Paseman, 2015.04.13
Apr
6
comment Referee reports not coming
R W, if you think it is a good question for the community, vote it up if you haven't done so. The vote count suggests to me that the question is in a gray area of community acceptance. Further, a citation may be needed to support the assertion of refereeing being more time consuming in mathematics than other areas (of science, I presume). I agree that the process might be different, but I imagine the author-journal interface is (on some level) very similar across refereed journals in all branches of science. Gerhard "References Referring To Referees Requested" Paseman, 2015.04.06
Apr
6
comment Referee reports not coming
Unfortunately, it is not about mathematics specifically. Even if you were to ask about the response time of a specific journal or field, this is still the wrong forum. If you have any academic contacts (former advisor, colleagues in the area), you would do well to ask them. If you are (like me) an outsider wishing to cultivate such contacts, this question on MathOverflow is a poor place to start. Gerhard "Other Ways And Other Days" Paseman, 2015.04.06
Apr
2
comment Polytopes whose intersections have few vertices
Welcome to MathOverflow! Perhaps they will make a "Human" badge for "edit on first post". Gerhard "Has Plenty Of Badges Already" Paseman, 2015.04.02
Apr
2
answered Counting zero-sum free sequences of a given length in $\mathbb{Z}_n$