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Jul
1
comment Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
@Assad that proof is indeed simple — but gives a proof only of a much weaker statement, AFAICS (only about dim=3)
Jun
27
comment Is this problem correct?
also a duplicate of math.stackexchange.com/q/25701
Jun
27
comment Show that $ \sum_{r=1}^{n-1}\binom{n-2}{r-1}r^{r-1}(n-r)^{n-r-2}= n^{n-2} $
That's called Abel[-Hurwitz] identity, I believe.
Jun
24
comment Strehl identity for the sum of cubes of binomial coefficients
Nice. Since you don't really use change of variables etc one can get rid of all integrals and get a slightly shorter version in the language of gen. functions.
Jun
24
comment Strehl identity for the sum of cubes of binomial coefficients
Thank you, I'll take a look
Jun
23
comment Where to find Yuri Manin's “Lectures on zeta functions and motives”
mpim-bonn.mpg.de/preblob/4793
Jun
20
comment Recurrence $(n+2)\text{Cat}_{n+1}=(4n+2)\text{Cat}_n$ for non-crossing matchings
Understanding is its own reward.
Jun
17
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
See also an example of using Jacobi sums to count points on $y^2=x^3-x$.
Jun
15
comment Counting the number of solutions of equation $x^2 + y^2 = 1$ over $\Bbb Z/p$
1) «Rational parametrization of conics»; 2) «Jacobi sums».
Jun
15
comment $SL_2(\mathbb Z_3)/Z(SL_2(\mathbb Z_3)) \cong \mathbb A_4$
From geometric POV the homomorphism to $A_4$ comes from the action of $SL_2(\mathbb Z_3)$ on 4-element set $P^1(\mathbb Z_3)$ (by fractional-linear transformations, if you will). Cf. $PSL_2(\mathbb F_4)\cong A_5$ etc.
Jun
7
comment Proof of $\sum_{n=1}^\infty \frac{1}{n^4 \binom{2n}{n}}=\frac{17\pi^4}{3240}$
related: math.stackexchange.com/q/144985
Jun
4
comment Why universal G-bundles are contractible?
If $B$ represents the functor «$X$ → principal $G$-bundles on $X$», then $E$ represents the functor «$X$ → principal $G$-bundles on $X$ with a fixed section». This functor is trivial, so $E$ is contractible.
May
14
comment Expected number of returns by time n in a symmetric 1-d random walk?
possible duplicate of Expected number of returns to zero in a symmetric random walk - closed form
May
13
comment Proving that $SL_2(\mathbb{Z}_5) / \{\pm I\}\simeq A_5$
cf. math.stackexchange.com/q/93762/152
May
6
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
...but extracting something explicit for HL polynomials from that doesn't look like an easy task...
May
6
comment Combinatorial definition of Hall–Littlewood polynomials (sum over SSYT?)
Wikipedia page on Macdonald polynomials a) doesn't contain words 'semi-standard' or 'augmented'; b) doesn't give a combinatorial description of Macdonald polynomials — it mentions a description of transformed Macdonald polynomials that uses 'certain combinatorial statistics' inv and maj. I guess details can be found in arxiv.org/abs/math/0409538
Apr
10
comment A reference for a combinatorial identity
The second form looks like just a Vandermonde's identity ($\binom{i+k-1}i=\pm\binom{-k}i$ etc).
Apr
8
comment Stiefel-Whitney classes with Z-coefficients
(Re: The only problem I see is with the Steenrod square operation which may be undefined for integral coefficients) Well, yes there are no non-trivial stable operations from H(-;Q) to H(-;Q), after all...
Mar
31
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@Stefan (Re: last comment) No-no, I want a counter example where X is not Hausdorff (and $Y$ is locally compact).
Mar
30
comment Counter-example to exponential law for locally compact [non-Hausdorff] spaces
@user87690 Right, thank you (if one assumes a strong enough version of local compactness — for non-Hausdorff spaces there are different versions of the definition — one needn't assume that $Y$ is Hausdorff — I've updated the question).