bio | website | math.ucla.edu/~pak |
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location | Los Angeles, CA | |
age | ||
visits | member for | 5 years, 5 months |
seen | 20 mins ago | |
stats | profile views | 8,959 |
My work page. My personal blog.
Jul 24 |
revised |
What are some examples of interesting uses of the theory of combinatorial species?
link updated |
May 28 |
answered | Complexity of planar scissor congruence |
May 17 |
awarded | Good Answer |
May 10 |
revised |
Random Alternating Permutations
update |
May 2 |
awarded | Autobiographer |
Apr 27 |
awarded | Good Question |
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 |