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Jan
29
comment Direct proof that a certain generating function is D-finite
I don't see what exactly is the question. 1) The algebraic equation (AE) is easy, as you write. 2) Getting ODE from AE is easy - it's repeated differentiation + linear algebra (see Stanley, Enumerative Combinatorics, Ch. 6). So getting the ODE in class explicitly is just as instructional as inverting a matrix or multiplying large numbers. I usually do this for somewhat simpler examples and leave such calculations to a computer or for students to do at home. Why would there be another way?
Jan
7
awarded  Custodian
Jan
7
reviewed Close 3_partite graphs
Jan
5
comment How to cite authors from any country correctly?
@Tim Chow -- good point. I guess I would use the original name X in the citation and in the body of the paper use "as proved by Y (nee X) in [X], we have.."
Jan
5
comment How to cite authors from any country correctly?
@Alexandre Eremenko -- this is my point, actually. How is the person supposed to search for "Oleĭnik" in the MathSciNet if one cannot type it? You search for "Oleinik" and find the right paper.
Jan
5
comment How to cite authors from any country correctly?
Not really. I recommend google test. Alternatively, MathSciNet has a preferred spelling, listing all other spellings in the author profile under "Published as"
Jan
5
answered How to cite authors from any country correctly?
Dec
13
comment Applications of Representation Theory in Combinatorics
Yes. It follows from definition of the Kronecker coefficients.
Dec
13
answered Applications of Representation Theory in Combinatorics
Dec
1
awarded  Nice Answer
Oct
13
awarded  Nice Answer
Sep
13
awarded  Enlightened
Sep
13
awarded  Nice Answer
Sep
13
awarded  Nice Answer
Sep
13
awarded  Nice Answer
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.