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May
17
comment Proving $\sum_{k=1}^{n}\binom{n-1}{k-1}{\binom{n+k}{k}}^{-1}=\frac 12$ combinatorially
Since both sums have non-integral terms, it's not entirely clear what kind of combinatorial argument are you looking for...
May
14
comment Is Frobenius the only magical automorphism?
In the last proof $R\to R$ should be $R\to R_{\sigma^n}$, right?
May
13
comment How can I find $\sum\limits_{n=i+1}^\infty \binom{n-1}{i}\left (\frac{1}{3}\right)^{n}$?
en.wikipedia.org/wiki/Binomial_series#Special_cases
May
13
comment Restrictions on the coefficients that allow a polynomial in a field of characteristic 0 to be solvable by radicals and the associated formula.
An irreducible polynomial equation is solvable iff its Galois group is solvable — if this doesn't answer you question, what is you question exactly?
May
13
comment Finding a Monoid
Well, this is just colimit of sets of possible matrix ranks — i.e. of sets $\{0,...,n\}$ (wrt obvious inclusions) — and such colimit is just a union of all these sets
May
13
comment Finding a Monoid
Well, yes, it's path-connected, so $\pi_0$ is a 1-element set. Now you have to prove that all sets $\{A^2=A,\operatorname{rk}(A)=k\}\subset IM_n$ are path-connected, and basically you're done.
May
13
comment Finding a Monoid
Can you find, say, $\pi_0 GL_n(\mathbb C)$?
May
13
comment Trigonometric identity involving sum of “Dirichlet kernel like” fractions
Oh, seeing the word 'induction' I haven't tried to read your answer before — but now I see that my solution is essentially the same...
May
13
comment Finding a Monoid
well, that's a very simple colimit actually; but before taking colimits — can you find $\pi_0\mathop{\mathcal I}(M_n(\mathbb C))$?
May
13
comment Finding a Monoid
idempotent = projection on a subspace...
May
13
comment Verifying Touchard's Identity
What do you mean by «progress from here on»? — the linked page contains (a sketch of) a proof. If you don't understand the plan, perhaps you should read some general introduction to generating functions; otherwise — try to follow it.
May
13
comment Trigonometric identity involving sum of “Dirichlet kernel like” fractions
(Re: «Dirichlet kernel like») maybe «Fejér kernel like»...
May
12
comment Verifying Touchard's Identity
...and a bijective proof follows from arXiv:math/0406381, I believe
May
12
comment Verifying Touchard's Identity
Have you tried reading Wikipedia?
May
10
comment Literature to the ring $\mathbb{Z}[\phi]$ where $\phi=\frac{1+\sqrt{5}}{2}$ is the golden ratio
Related: Golden Number Theory
May
10
comment Example of an extension group
If the sequence goes in this direction that's called «an extension of $Q$ by $K$», not the other way round.
May
9
comment Geometric picture of Stiefel-Whitney class of a tangent bundle?
I can't resist mentioning that $w_2$ is the obstruction to existence of a spin structure.
May
9
comment Geometric picture of Stiefel-Whitney class of a tangent bundle?
One more reference is, of course, Milnor, Stasheff. Characteristic Classes
May
9
comment Motivation for the study of amoebas.
AFAIK, one area where amoebae appear is (random) dimer configurations (see papers of Kenyon &co — e.g. Dimers and Amoebae or (perhaps, better) Lectures on Dimers).
May
9
comment Motivation for the study of amoebas.
@Fredrik Well, tropical geometry gives a lot of reasons to study tropical curves; tropical curves are, of course, degenerate amoebae — (which explains the relation of tropical geometry to usual one, but) that doesn't quite explain why «real» (i.e. not degenerate) amoebae are interesting...