bio | website | math.ucla.edu/~pak |
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location | Los Angeles, CA | |
age | ||
visits | member for | 5 years, 6 months |
seen | 1 hour ago | |
stats | profile views | 9,010 |
My work page. My personal blog.
Aug
24 |
comment |
Important formulas in Combinatorics
Um, we gave a truly bijective proof of MMT in this paper, section 2. Sorry for the self-promotion. arxiv.org/abs/math/0607737 |
Aug
20 |
comment |
Important formulas in Combinatorics
Sam, you are right. Sometimes the names are misleading... |
Aug
19 |
comment |
Important formulas in Combinatorics
I think we agree on everything except "what is a formula". It's not really a formal discussion, but if this is a formula, then so is every theorem in combinatorics. |
Aug
18 |
comment |
Important formulas in Combinatorics
Yeah, well - this identity is truly classical and extremely important in Partition Theory (see also Hardy & Wright Number Theory book on this). Your statement is sort of like saying "matrices are important especially because SU(3) helps explain quarks". True, but a minority view. |
Aug
18 |
comment |
Important formulas in Combinatorics
Um, no. They were originally defined and studied as multiplicity constants in the tensor product of two GL(n,C) modules. Those are non-negative integers by definition. A combinatorial interpretation came much later indeed, but that speaks to the importance (which I agree with completely), not whether this is a formula akin the HLF. |
Aug
18 |
comment |
Important formulas in Combinatorics
That's not a formula in a sense that it does not allow computing LR coeff. faster than via the other standard definitions. |
Aug
18 |
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Important formulas in Combinatorics
The Jacobi triple product identity was proved bijectively by Sylvester (see my partition bijections survey). Reviewing the literature I found about 11 proofs by others, all equivalent but phrased differently. Your answer suggests that "particle sea" proof is somehow different and modern. It is in fact equivalent to the original Sylvester's bijection. |
Aug
4 |
awarded | Good Answer |
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 |