bio | website | grpaseman.wordpress.com |
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location | S.F. Bay Area | |
age | ||
visits | member for | 4 years, 9 months |
seen | Oct 15 at 20:12 | |
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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)
Oct 3 |
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Prime divisors of the respectively minimal binomial coefficients
Wlod, I only see that Mersenne primes prevent the definability of G(2). Indeed, I believe one can prove B(2)=4 and I think it is not hard to show B(3) and G(3) exist and are larger than 8, but not by much. Gerhard "Or We're On Different Pages" Paseman, 2014.10.03 |
Oct 2 |
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Prime divisors of the respectively minimal binomial coefficients
You should also consider B(n) and G(n), which are the smallest values of b and g such that for all c >= b or h >= g, one has c choose n have at least n different prime divisors or h choose n have at least n different prime divisors greater than n. Stoermer's Theorem suggests to me that these values also exist. Gerhard "Wants Really Explicit Application Scope" Paseman, 2014.10.01 |
Oct 1 |
answered | what-if.xkcd.com: stabbing (simply connected) regions on the 2-sphere with few geodesics |
Oct 1 |
answered | Has philosophy ever clarified mathematics? |
Sep 29 |
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a colouring / matching problem
Also, I am interested in just tackling the problem instance; I doubt I will come up with anything not already considered twenty or more years ago by people working on PARTITION. But perhaps you can tell me the following: by focussing on (only those boxes having) number 11, then number 11 and 13, then 11,13,12, then 11,13,12,0, it looks like the number of valid colorings is bounded above by 1, 4 , g=4*(11!)/((2!)4!5!), g*(10!)/4!. As we add more numbers, does the number of valid colorings explode or level off? Gerhard "Picking The Problem Into Pieces" Paseman, 2014.09.29 |
Sep 29 |
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a colouring / matching problem
I'm thinking more about shortening: consider a coloring partly successful if it manages to color the boxes based on just the numbers 0-k for some positive integer k (or pick your favorite subset of 0-14). A short proof of infeasibility may arise from just attempting the colors 0-7. Ideally, for each coloring of the smallest boxes, toss out those colors and labels, and look for a feasible coloring of the remainder. Now shorten the vectors and see if an infeasibility proof arises from just looking at numbers 0 through 7, say. Gerhard "Merging Is Different From This" Paseman, 2014.09.29 |
Sep 29 |
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a colouring / matching problem
@Martin, how many mod 8 feasible colorings are there of the "smallest" boxes? In other words, how many ways are there of coloring the two boxes of two items and the four boxes of four items in such a way that when you are done, the remaining colors are each a multiple of 8? Also, do the "big" boxes fall into nice groups like half the boxes have numbers 1,2,3,4, 30% have numbers 6,7,8,10, and a much smaller remainder have some scattering? It may be that looking at the first six coordinates will suggest a coloring for the rest. Gerhard "Slicing Diagonally Might Also Help" Paseman, 2014.09.28 |
Sep 25 |
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a colouring / matching problem
If all the colors had a multiple of 8 labels, but every feasible coloring involved coloring the 2 distinct boxes of 2 items with different colors, you would get a mod 4 or mod 8 conflict. You can look for parity conflicts this way, or assume that they have to be resolved first and thus limit the available colorings of the "smallest" 13 boxes. At the moment, I see no other easy way to find a proof of infeasibility. Gerhard "Maybe Subtract Off Symmetric Boxes" Paseman, 2014.09.24 |
Sep 24 |
awarded | Autobiographer |
Sep 19 |
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Prime Hadamard Matrices
@Gerry, Peter Keevash's recent paper suggests that there may be only finitely many such n with 4n not the order of a real Hadamard matrix. Of course, complex Hadamard matrices exist of all orders. I have not studied his paper enough to convince myself that it applies to Hadamard designs, but it looks promising. Gerhard "Still Puzzling Over Random Constructions" Paseman, 2014.09.19 |
Sep 19 |
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Representing a number close to 1 with a sum of reciprocals of natural numbers
Since your question is short, adding about twice as much ink after the question to explain motivation is welcome. If it gets to ten times as much ink, consider abbreviating the motivation and providing a link to an expanded version. I don't see adding a separate answer for it yet as a good thing. Gerhard "Or Measure It In Pixels" Paseman, 2014.09.19 |
Sep 19 |
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a colouring / matching problem
The above assumes there is a feasible solution you wish to find. If you want to prove that there is no feasible solution, I suspect finding a small infeasible subset of boxes is your best hope. Gerhard "Doesn't Like Infeasible So Much" Paseman, 2014.09.19 |
Sep 19 |
answered | a colouring / matching problem |
Aug 18 |
awarded | Nice Answer |
Jul 22 |
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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 |
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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 19 |
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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 |
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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 |
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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 |
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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 |