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Apr
8
comment Proof of the binomial identity $\displaystyle\binom{m}{n}=\sum_{k=0}^{\lfloor n/2 \rfloor} 2^{1-\delta_{k,n-k}} \binom{m/2}{k} \binom{m/2}{n-k}$
See also Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$? etc
Apr
8
comment Proof of the binomial identity $\displaystyle\binom{m}{n}=\sum_{k=0}^{\lfloor n/2 \rfloor} 2^{1-\delta_{k,n-k}} \binom{m/2}{k} \binom{m/2}{n-k}$
that's just a special case of en.wikipedia.org/wiki/Vandermonde%27s_identity
Dec
25
comment Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
coloured squares also can be counted visually: mathoverflow.net/questions/8846/proofs-without-words/8847#8847
Dec
14
comment How does one read $\bar{A}$ aloud in Russian?
«A с чертой» is frequently used (have never heard «A с надчеркиванием» in my life)
Nov
27
comment Using the Fano plane for octonion multiplication
related: What is the oriented Fano plane? @ MO
Oct
13
comment Source and/or combinatorial interpretation for $F_{n+k} = \sum_{i=0}^{k} \binom{k}{i}F_{n-i}$
cf. math.stackexchange.com/questions/112752
Oct
9
comment Another binomial coefficients sum
Related: math.stackexchange.com/q/1306605 & math.stackexchange.com/q/121407
Oct
3
comment Area of hyperbolic triangle definition
@KWSK Well, (hyperbolic) lengths of both the base and the (hyperbolic) perpedicular are manifestly invariant under hyperbolic motions.
Oct
3
comment Area of hyperbolic triangle definition
Well, one reason is that in hyperbolic geometry $ah_a\neq bh_b$, so this 'area' would depend on the side we choose as the base — so in a sense it's not well-defined.
Oct
3
comment Area of a right angled hyperbolic triangle as function of side lengths
Is $\tan(S/2)=\tanh(a/2)\tanh(b/2)$ nice enough?
Oct
1
comment Combinatorial interpretation of identity: $\sum_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$
(Re: generalization) indeed
Oct
1
comment Combinatorial interpretation of identity: $\sum_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$
@Darij, Alexander thank you — I hope I fixed the typos
Sep
19
comment A three variable binomial coefficient identity
@darij why, I already do (see par. 3 of 'Comments and thoughts' there)
Sep
12
comment Is any 2$m$-dimensional manifold almost complex?
locally — yes, globally — no
Aug
23
comment Is the functional equation for $\zeta (s) \left(1-\frac{1}{3^{s-1}}\right)$ known?
Yes, just change $2^{-s}$ to $3^{-s}$ (and $2^{-s-1}$ to $3^{-s-1}$) in the func. equations for $\eta$.
Aug
21
comment The form of the zeta function of an elliptic curve over a finite field
And of course a proof for $y^2=x^3-x$ goes back to Gauss (see e.g. Ireland, Rosen. A Classical Introduction to Modern Number Theory, ch. 8 for the proof)
Aug
21
comment The form of the zeta function of an elliptic curve over a finite field
Well, there is a relatively elementary proof in Silverman. The Arithmetic of Elliptic Curves
Aug
10
comment Cohomology of $K(\mathbb{Z}_2, n)$
See doc.rero.ch/record/482/files/Clement_these.pdf (including tables in Appendix C). In particular, yes, $H^5(K(Z/2,2))$ has 4-torsion, and no, I don't think there is a really simple and explicit answer.
Aug
9
comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)
related: math.stackexchange.com/q/1284161
Aug
9
comment A Geometric Proof of $\zeta(2)=\frac{\pi^2}6$? (and other integer inputs for the Zeta)
the link is dead...