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bio website math.ucla.edu/~pak
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visits member for 5 years, 5 months
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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