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1d
comment Cavalieri's principle and inversion of the Vandermonde matrix
See Roy Smith's mathoverflow.net/questions/28268/do-you-read-the-masters/…
Jan
26
comment Inversion, Koszul duality, combinatorics and geometry
Moderators, community wiki?
Jan
26
asked Inversion, Koszul duality, combinatorics and geometry
Jan
23
comment What is a good introduction to cluster algebras from surfaces?
I'll leave it open, if you don't mind, to encourage someone to find another good paper.
Jan
23
comment Why complete symmetric polynomials and elementary symmetric polynomials are dual to each other?
Thanks, but I'm simply looking for how the concept of Koszulness could inform me of the combinatorics/geometry of the reciprocal identity (as in, say, OEIS A133314). These inverse relations (multiplicative, compositional, umbral compositional) always seem to contain a lot of underlying combinatorics and often geometry.
Jan
22
comment Origin of terms “flag”, “flag manifold”, “flag variety”?
View the Wiki article on pennant and note flags for naval ships. See etymology of pennant from perhaps pennon etymonline.com/index.php?term=pennon&allowed_in_frame=0
Jan
22
comment Origin of terms “flag”, “flag manifold”, “flag variety”?
Interesting that you came up with the same idea as my comment a day before your post. The idea must be in the air, I suppose.
Jan
21
comment Why complete symmetric polynomials and elementary symmetric polynomials are dual to each other?
I'm familiar with the identity you state, Newton identities relating the symmetric polynomials, relation to determinants, etc., but not with Koszul complexes. Can you give me a reference at the most elementary level you are aware of that elaborates on the Koszul complex and its relation to the reciprocal identity?
Jan
20
comment What is a good introduction to cluster algebras from surfaces?
You've, of course, checked out the two intros by L. Williams and B. Keller. Have you reviewed these lectures math.berkeley.edu/~williams/CA.html ?
Jan
20
comment What is a good introduction to cluster algebras from surfaces?
sciencedirect.com/science/article/pii/S0001870809003387 ?
Jan
19
comment Origin of terms “flag”, “flag manifold”, “flag variety”?
Regardless of the actual etymology and original visualization, equating flag with (triangular) pennant instantly evokes associations with triangular matrices and projections to a point in projective geometry.
Jan
17
comment In “splendid isolation”
See this reference arxiv.org/abs/quant-ph/0404009 from the Wiki article.
Jan
17
comment In “splendid isolation”
And in classical mechanics with the non-commuting Euler-angle matrices for rotations in 3-D, with which they must have been familiar, so, looking at the notes in the Wikipedia article on matrix mechanics, maybe the difficulty was in making the connection between what was initially regarded as an infinite "Fourier" series expansion for transition spectra and a pair of infinite matrices representing non-commuting ops. It seems Born was prepared by earlier work to make the explicit connections to algebraic manipulations of infinite matrices.
Jan
15
comment Why do Bernoulli numbers arise everywhere?
The series formula for zeta above involves the base number sequence for the generalized Bernoulli polynomials of the second order, whose asymptotics show the the series above must be an asymptotic expansion. ----- The MOQ link above for the Hirzebruch genera no longer contains my answers. I transferred them to my website, where I can refine and expand on them.
Jan
13
comment Alternative definition of the Lagrange Inversion formula
See for example this mathoverflow.net/questions/145555/…. This method for finding the comp inverse can be applied to formal power series and allows formulations in different "coordinate/indeterminate" systems related to very interesting combinatorics. Very old method at least as far back as the first half of the 1800s.
Jan
12
awarded  Yearling
Jan
10
comment Max/min problems related to associahedra or their duals (ions on balls revisited)
The dual for the 3-D associahedron is depicted in en.m.wikipedia.org/wiki/Triaugmented_triangular_prism.
Jan
9
comment A mysterious Heisenberg algebra identity from Sylvester, 1867
See math.stackexchange.com/questions/191752/… for a short, simple intro to the umbral notation I use.
Jan
8
comment Newton series and Fourier transform - is there an analogy?
Looking at fractional integroderivatives of Laplace-transform type and their convolutional and related Cauchy-type integrals leads to another interpolation formula.
Jan
8
comment Newton series and Fourier transform - is there an analogy?
For the last section, identify $g(-x)$ with $f(x)$ to relate it to your formula.