Grigory M
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# 795 Comments

 Jan 16 comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$? OK, I apologise — this question was not completely clear as written — but it's a) not a duplicate of the linked question; b) can be reasonably answered. Jan 16 comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$? Jan 15 comment Unimodality of q-binomial coefficients Unimodality of q-binomial coefficients is a difficult theorem, proved more than 20 years after it was conjectured. If you're really interested in a proof — it's easy to google references. Jan 15 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ @655321 though there is one example that is explained in detail in many books (e.g. in Enumerative Combinatorics): Lagrange inversion formula Jan 15 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ @655321 I'm afraid I don't know a good reference... Jan 14 comment Embedding of two-dimensional CW complexes which induces a zero homomorphism on second homotopy groups x-posted to MO: mathoverflow.net/q/193845 Jan 14 comment When $\frac{C(n, k)}{n^{k-1}} > 1$? Well, for $n=k!+t$ we need to compare $(1+t/k!)\cdot(1-1/(k!+t))(1-2/(k!+t))\ldots(1-(k-1)/(k!+t))$ withs 1. Shouldn't be hard (take logarithm, bound it...) — and at least genesis of $s_k$ is clear. Jan 13 comment Summation with Binomial Coefficients, $\sum (-1)^k \binom{m_1}{k} \binom{m_2}{k}$ Jan 13 comment Solve easy sums with Binomial Coefficient possible duplicate of Understanding a combinatorial relation. Jan 13 comment Summation with Binomial Coefficients, $\sum (-1)^k \binom{m_1}{k} \binom{m_2}{k}$ related: $\sum(-1)^k\binom mk^2$ Jan 12 comment Groups with no nontrivial topology (Re: «I am quite interested in how the problem changes if G is infinite or finite.») That's easy to answer: changes from completely trivial (finite) to very hard problem that stayed open for almost 40 years (infinite). Jan 12 comment Groups with no nontrivial topology Jan 10 comment Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$? related: math.stackexchange.com/q/199691 Jan 9 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ off the top of my head, something like math.stackexchange.com/a/609202 should work (but finding a bijective proof would be, perhaps, more challenging) Jan 9 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ @Marko tomorrow (or later) — maybe; if you have time now — please just go ahead Jan 9 comment A three variable binomial coefficient identity Thank you! I'm awarding the bounty now — and will try to understand the proof later. Jan 9 comment A three variable binomial coefficient identity I've also asked a (different but) related question @ MO Jan 9 comment Is this morphism of spectra zero in the stable homotopy category? No, that generalization is not true: take any non-trivial stable cohomological operation — say, Bockstein $EM(n)\to EM(n+1)$. Jan 8 comment Kernel and image of a homomorphism $SL(2,5)\to S_5$ Jan 7 comment A three variable binomial coefficient identity I now suspect that both sides count 00-avoiding $3n$-periodic binary sequences with exactly $n$ zeroes — maybe someone can prove it?