Grigory M
Reputation
11,615
365/400 score
 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 $SL_2(\mathbb{Z}_5) / \{\pm I\}\simeq A_5$ 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).