bio | website | math.ucla.edu/~pak |
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location | Los Angeles, CA | |
age | ||
visits | member for | 5 years, 2 months |
seen | 3 hours ago | |
stats | profile views | 8,765 |
Apr 21 |
awarded | Promoter |
Apr 15 |
awarded | Curious |
Apr 14 |
comment |
3-colorings of the unit distance graph of $\Bbb R^3$
@JMPerry - Yes. Every triangle in $\Gamma$ has all sides unit length. |
Apr 14 |
comment |
3-colorings of the unit distance graph of $\Bbb R^3$
@JMPerry. I don't understand your question/objection. Please write it in full if possible. |
Apr 14 |
comment |
3-colorings of the unit distance graph of $\Bbb R^3$
@JMPerry - No, since $2\beta \neq 1$. I meant to write "unit length triangle" in my comment above, which would mean it's a triangle in $\Gamma$. |
Apr 14 |
revised |
3-colorings of the unit distance graph of $\Bbb R^3$
added 12 characters in body |
Apr 14 |
comment |
3-colorings of the unit distance graph of $\Bbb R^3$
@TimChow. As I say in the note, this is not an important condition - we will be happy with any $\alpha$. However, we can rule out some values such as $\alpha = 1/\sqrt{2}$ when (ABCD) is a square - it's easy to see that such coloring does not extend from (ABCD) to $\Bbb R^3$. We cannot rule out any transcendental values. |
Apr 14 |
comment |
3-colorings of the unit distance graph of $\Bbb R^3$
@JMPerry - Not sure what you are asking. Main condition: every triangle must be non-rainbow, i.e. have at most 2 colors. Without (ABCD) one can just take a monochromatic coloring of the whole space. |
Apr 14 |
awarded | Nice Question |
Apr 14 |
revised |
3-colorings of the unit distance graph of $\Bbb R^3$
clarification |
Apr 14 |
revised |
3-colorings of the unit distance graph of $\Bbb R^3$
note added |
Apr 14 |
revised |
3-colorings of the unit distance graph of $\Bbb R^3$
edited body |
Apr 14 |
asked | 3-colorings of the unit distance graph of $\Bbb R^3$ |
Apr 14 |
revised |
Fundamental Examples
Catalan numbers were introduced by Euler in the second half of 18th entury |
Mar 28 |
revised |
Not especially famous, long-open problems which anyone can understand
reference to an article |
Mar 20 |
revised |
generating set for symmetric group $S_n$
added 35 characters in body |
Mar 19 |
answered | generating set for symmetric group $S_n$ |
Mar 1 |
comment |
3D models of the unfoldings of the hypercube?
You might like a movie on the 2D case: etudes.ru/ru/etudes/cubisme |
Feb 22 |
awarded | Nice Question |
Feb 21 |
revised |
Linear groups which don't contain products of free groups
rewording |