bio | website | research.microsoft.com/~cohn |
---|---|---|
location | Cambridge, MA | |
age | 40 | |
visits | member for | 4 years, 4 months |
seen | 8 hours ago | |
stats | profile views | 3,893 |
Jun 22 |
comment |
polynomial with rational coefficients
@ToddTrimble: I see how to do this if $f(n)$ is an integer for all $n$, but how do you handle the case where this is true for some arbitrary infinite set? (I may be missing something obvious.) |
Jun 22 |
comment |
polynomial with rational coefficients
Maybe I'm missing a nice way to do it via calculus of finite differences, but that feels like overkill to me. If $f$ has degree $d$, then it's determined by its values at $d+1$ points, and polynomial interpolation preserves rationality. |
May 25 |
awarded | Enlightened |
May 24 |
awarded | Nice Answer |
May 24 |
answered | Can the Legendre symbol be calculated in polynomial time? |
May 17 |
comment |
What is known about $\displaystyle \sum_k{a^{b^k}}$?
If $b$ is an integer and $a$ is the reciprocal of an integer, then you get a beautiful continued fraction expansion (see the articles dx.doi.org/10.1016/0022-314X(79)90040-4 and dx.doi.org/10.1016/0022-314X(82)90047-6 by Jeffrey Shallit). |
Apr 23 |
comment |
Is anything known about which numbers appear in the continued fraction expansion of $\pi$?
Hopefully someone can expand on this (to make it more suitable as a formal answer), but the quick version is yes: (a) and (b) were true in 1978 and remain true today. |
Apr 21 |
comment |
Why can't there be a problem both in P and NPC
You're right that the illustration you link to assumes that P ≠ NP. Note that on the P versus NP Wikipedia page, it has the caption "Diagram of complexity classes provided that P ≠ NP." |
Apr 19 |
awarded | Enlightened |
Apr 18 |
revised |
I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
corrected reference, added link |
Apr 18 |
awarded | Nice Answer |
Apr 18 |
revised |
I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension
made continuity hypothesis explicit |
Apr 18 |
answered | I would like to have a counter example that Peano's theorem does not apply to spaces with infinite dimension |
Apr 15 |
comment |
Limit of distance between two random points in a unit-radius $n$-sphere
I'm not sure there's such a contrast between cubes and spheres. In high dimensions a unit cube is vastly larger than a unit sphere, as measured by diameter or volume, so it's not as fair a comparison as the word "unit" suggests. |
Apr 12 |
comment |
Geometric explanation of Hutton's formula?
Roger Nelsen gave a proof without words in Math Magazine 86 (2013), 350. See www.jstor.org/stable/10.4169/math.mag.86.5.350. |
Mar 21 |
answered | Theta series for the Leech lattice |
Mar 18 |
awarded | Yearling |
Mar 17 |
answered | Inequality for Laguerre polynomials |
Mar 16 |
comment |
Analogues of P vs. NP in the history of mathematics
I didn't downvote it myself, but since no other explanation seems to be forthcoming: the runtime fence problem for TMs fails to satisfy Scott's second criterion ("Mathematicians conjectured that the two classes were unequal, but were unable to prove or disprove that for a long time..."), since Viola gave a proof 20 minutes after you posted the question on cstheory.stackexchange.com. I don't really understand what you mean by the runtime fence problem for languages, but it apparently doesn't satisfy the third criterion ("Eventually, the conjecture was either proved or disproved"). |
Feb 11 |
comment |
What does a Zonal sphere harmonic look like?
Is there an explicit formula for the $L^p$ norms of zonal spherical harmonics? The paper faculty.fiu.edu/~decarlil/Preprints/Proc4.pdf proves estimates for them, which suggests that no such formula is known. |