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bio website grpaseman.wordpress.com
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visits member for 5 years, 5 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)


2h
comment binomial/factorial identity mod p
I don't think you need to restrict b at all. Or is b a typo for c? Gerhard "Go For Even Greater Generality" Paseman, 2015.07.01
2h
comment binomial/factorial identity mod p
Do you know of Kummer's theorem (or Lucas's theorem) on binomial coefficients? I think it would be a consequence of one of those. Gerhard "Don't Have A Literature Reference" Paseman, 2015.07.01
5h
comment Number of prime numbers in a range
If the prime k-tuples conjecture holds, it may be that for infinitely many n that A_n is larger than (log n) /(log log n). Gerhard "Still Too Early To Tell" Paseman, 2015.07.01
7h
comment Bound on $g(n+1)/g(n)$ for Landau's function
Nice and sharp. Once you find out how big a power of two is needed, say $c$ many, you can later establish something like $g(n) \geq g(n + 2^{c-1})/2$. Gerhard "Perhaps Already In The Literature" Paseman, 2015.07.01
8h
comment Simultaneous lcms
Gee Max, you make it look so easy. Gerhard "Unready To Compute Stirling Numbers" Paseman, 2015.07.01
8h
answered Simultaneous lcms
22h
answered A conjecture on the prime counting function
23h
comment A conjecture on the prime counting function
It might be great, but it is unlikely. There might be more refined versions of the conjecture in connection with Goldbach's binary conjecture. However, primes fluctuate wildly enough that I would only expect either relation to hold with x and y separated by a significant power of x. For a start, check out texts by Hans Riesel and by Paulo Ribenboim on primes. That and much experimentation may give you a feel for plausible conjectures on distribution of primes. Gerhard "Feels His Way Around Primes" Paseman, 2015.06.30
23h
comment A conjecture on the prime counting function
If you think about how such a conjecture could fail, you could imagine a dense constellation of primes between x and (x+y)/2 and very few primes between (x+y)/2 and y In fact, it is likely that both conjectures fail infinitely often, and conjecture 2 certainly fails for x=y. You might consider running a computer program to check your conjecture for a few million pairs (x,y), to see how it fails. Gerhard "Ask Me About Prime Gaps" Paseman, 2015.06.30
2d
answered When is a sequence the sum of two Beatty sequences?
Jun
27
comment A curious determinantal inequality
Perhaps it is easier if we remove square roots? Rewriting, I get det(A^4 + ABBA + BAAB + B^4) >= det(A^4 +AABB + BBAA + B^4). While temptingly pleasing, I don't know if positive definite is enough of a restriction to carry this through. Are there similar ineqaulities which are true and motivating? Gerhard "Don't Know About Hermitian Matrices" Paseman, 2015.06.27
Jun
25
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
The basic intent, of finding out whether the paper is correct, is indeed of interest. That does not mean that it is appropriate for MathOverflow, just as conjectural discussion of Mochizuki's proof of the ABC conjecture and other examples are not appropriate. The previous questions address some of the mathematics and reasons for why the statement might be true or false. The question here does not, and can be viewed as damaging to the author and (more importantly) to MathOverflow. I don't challenge the intent so much as the form. Gerhard "Maybe I Should Just Edit" Paseman, 2015.06.24
Jun
24
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
Using arXiv trackbacks, one finds other questions and comments on MathOverflow that may be useful in gauging the quality of this paper. If I were the author, I would prefer someone pointing out a specific problem in the current version rather than pointing to older versions and suggesting that insufficient improvements had been made. Gerhard "Treat Authors With Respect Too" Paseman, 2015.06.24
Jun
24
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
At this current writing, the question is not of the quality I would like to see on MathOverflow. It renders a subjective opinion which may be correct but I will not know without doing some extensive effort. Francesco, If I recall a preprint of yours from ten years ago, and notice a recent publication of a similar paper by you, how appropriate is it for me to publicly claim "Ten years ago it needed a lot of work; can it possibly have gotten publishable?" MathOverflow is not for critiquing papers; it is for answering questions. Gerhard "Let's Not Talk About Publishers" Paseman, 2015.06.24
Jun
24
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
This is the wrong forum for your question. This kind of question falls in my view to discussing of preprints. If you find a particular error and want confirmation of that error, you might ask about that specific detail. I would avoid editorializing or commenting on the quality of the paper; it should be enough to get people to recognize a serious defect in the paper, if one exists. Gerhard "Treat All Papers With Respect" Paseman, 2015.06.24
Jun
22
comment Minimum rank of certain matrices
I don't know if it is the largest. If you post details in your question, I can think about it and try to improve upon it. Gerhard "Ask Me About Binary Matrices" Paseman, 2015.06.22
Jun
22
comment Minimum rank of certain matrices
Not obviously, as the matrices are square and both rows and columns have to be distinct. Gerhard "Read The Fine Print, Please" Paseman, 2015.06.22
Jun
22
comment Minimum rank of certain matrices
It is easy to produce rank of 2n/3 and probably less than log(n) for n sufficiently large. Take a "diagonal" subspace of R^n that includes the all ones vector, for example. Gerhard "Many Ways To Lose Weight" Paseman, 2015.06.22
Jun
20
comment Proving a differential inequality without performing iteration
It might be fun to try a different iteration: multiply by g, get (g^2 / 2)' bounded from above by g^(3/2), write h for g^2/2, get h' <= 2h^(3/4), multiply by h to get (h^2/2)' <= 2h^(7/4), and so on to get something that might tend to j' <= cj - epsilon, and then work you're way back down. Gerhard "It's Like Riding A Swing" Paseman, 2015.06.18
Jun
17
comment Style of mathematical writing vs. too many lemmas
Terry Tao has part of his blog devoted to writing. He includes links to many other opinions, including notes on a course by Knuth and others on mathematical writing. If the original poster has exhausted that resource and still has a question on what to do, they might then come back here with a more specific request than "Any ideas?" Gerhard "The Internet Has Your Answer" Paseman, 2015.06.16