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bio website math.ucla.edu/~pak
location Los Angeles, CA
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visits member for 5 years, 2 months
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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