10,265 reputation
33066
bio website
location Moscow, Russia
age
visits member for 4 years, 1 month
seen 8 hours ago

umagon at google mail


Oct
28
comment Proving the binomial coefficient identity $\binom{~s + t~ }{s} = \prod_{i=1}^s \prod_{j=1}^t \frac{i + j}{i + j - 1}$
Cf. en.wikipedia.org/wiki/Plane_partition#MacMahon_formula BTW
Oct
14
comment Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
math.stackexchange.com/q/918/152
Sep
19
comment Putting ${n \choose 0} + {n \choose 5} + {n \choose 10} + \cdots + {n \choose 5k} + \cdots$ in a closed form
related: math.stackexchange.com/q/1382/152
Aug
30
comment Which manifolds are parallelizable?
@Mikola 1-skeleton of X
Aug
27
comment Is there a standard name for a category all of whose contravariant hom functors are sheaves?
What do you mean by a sheaf on arbitrary category? (One needs a Grothendieck topology on category to speak about sheaves. Well, any category has a Grothendieck topology in which all representable functors are sheaves.)
Aug
24
comment Simplifying the sum with binomial coefficients
See also math.stackexchange.com/q/80649/152
Aug
21
comment Direct proof of Gelfand-Zetlin identity
See also: I. Gessel. Binomial determinants, paths, and hook length formulae in Adv. Math. (from non-intersecting paths to binomial determinant and computation of binomial determinant).
Mar
6
comment Gessel-Viennot Method
cf. math.stackexchange.com/questions/3363/…
Feb
13
comment Decomposition of vector bundles over a CW complex
"My first thougt was to use..." -- yes, that's right, just do it!
Feb
10
comment An application of Yoneda Lemma
@Loronegro Notation is completely standard. I doubt, anyone unfamiliar with it would be able to answer the question, anyway.
Feb
8
comment Collatz Conjecture proof for review.
Numerous incorrect proofs of famous open problems is not what Math.SE is for -- voted to close as "too localized".
Jan
29
comment How to understand the diagonal approximation?
Brown gives both motivation and an example (in exercise). What is your question, exactly? (Besides "I feel hard to understand it" and "Who can help me?".)
Jan
26
comment Gauss-type sums for cube roots
(Actually, first I wanted to ask about "Gauss-sum-type" formulas for roots of a cubic polynomial with perfect square discriminant -- but then thought that just cube roots should be more tractable.)
Jan
26
comment Why is this complex acyclic?
@Scott $K$ depends on choice of an element $x_0\in K$, if that's what you mean (general statement is that any cone is contractible and a simplex is a cone over any of it's vertices -- so one need to fix some choice).
Jan
25
comment Tensoring with vector bundle is a dense endofunctor of $D^b(\text{coh }X) $?
Yes, exactly (it splits because this map has section coming from $V\otimes V^\vee\cong hom(V,V)\ni Id$).
Jan
20
comment The status of $\mathbb{R}$ in homotopy theory.
(somewhat) related: mathoverflow.net/questions/28380/…
Jan
20
comment Cohomology ring $H^*(\mathbb{R}P^3 \# \mathbb{R}P^3; \mathbb{Z}_2)$.
you can just edit earlier post instead of posting updated version as a separate question
Jan
20
comment Cohomology ring $H^*(\mathbb{R}P^3 \# \mathbb{R}P^3; \mathbb{Z}_2)$.
possible duplicate of computing cohomology algebra of connected sum of two real projective spaces
Jan
17
comment Which cohomology theories have a formula $\langle \Omega,\text d \omega \rangle = \langle \partial \Omega,\omega \rangle$?
@NickKidman There is standard definition of extraordinary (co)homology theory (Eilenberg-Steenrod axioms). If you mean something else -- what exactly?
Jan
16
comment Which cohomology theories have a formula $\langle \Omega,\text d \omega \rangle = \langle \partial \Omega,\omega \rangle$?
Do you mean in extraordinary cohomology theories?