9,905 reputation
13557
bio website research.microsoft.com/~cohn
location Cambridge, MA
age 40
visits member for 4 years, 7 months
seen 9 hours ago

1d
comment Who first defined quantum integers?
I believe Gauss introduced Gaussian binomial coefficients in 1811 in Summatio quarumdam serierum singularium. I just flipped quickly through it, and I couldn't see any explicit discussion of quantum integers per se, but Chris Godsil is certainly right that they are implicit since they are the special case $m$ choose $1$ (and in any case I might have missed some broader discussion).
Oct
3
comment Translative packing constant strictly larger than lattice packing constant
Yeah, I think it's very plausible that one could construct an example in a much lower dimension, and conceivable that one could prove it rigorously. I haven't thought much about how hard the difficulty of proving that a lattice packing is optimal varies with dimension (for convex bodies). The Betke-Henk paper deals beautifully with polyhedra in three dimensions, but I have no idea how hard four, five, or six dimensions would be.
Oct
3
comment Translative packing constant strictly larger than lattice packing constant
I don't know of an example, and I wouldn't be surprised if nobody knows one (but I'll be very pleased if I'm wrong about this).
Sep
30
awarded  Explainer
Aug
24
comment Time in Girard's Geometry of Interaction
My first thought upon seeing the question title was that it was going to be about mustard watches.
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.