Grigory M
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 Jan22 comment Curious Binomial Coefficient Identity Jan20 reviewed Close How to understand the regular cardinal? Jan20 reviewed Approve mantel theorem bipartite graphs, two triangles share an edge Jan19 reviewed Close I need help to evaluate this definite integral. Jan19 reviewed Close Solve 10 base logarithms Jan19 reviewed Close Forming equations for exponential growth/decay questions Jan19 comment Binomial Identity $\sum\binom{2n+1}{2k+1}\binom{m+k}{2n} = \binom{2m}{2n}$ see also math.stackexchange.com/q/1107465 for a bijective proof of an equivalent identity Jan19 comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$ come to think of it, substituting $a\to 2n+1$, $n\to 2m-2n$ (and $k\to m-2n+k$) one can see that these two identities are equivalent Jan19 comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$ Both identities are of the form $\sum_k\binom a{b-2k}\binom{c+k}d=\binom ef$ — and I strongly suspect there is a unified proof. Jan19 reviewed Looks OK Let $G$ be a group, and $H$ a subgroup of $G$. Let $a, b \in G$. Prove $Ha=Hb$ iff $ab^{-1} \in H$. Jan19 reviewed Leave Closed An endless loop in a program that search for mathematical theorems and proofs − a milestone? Jan19 reviewed Close Min, Max, Infimum, Supremum Jan19 reviewed Leave Open Given a general 3D Matrix operation … who can I apply “1/2” of the effect of it ? Jan19 reviewed Looks OK Find prime factorization of $2^{22} + 1$ Jan19 reviewed Close cohomology ring of a quotient space Jan18 reviewed Close Simplify the radical expression Jan18 reviewed Reject Fallacy of denying the hypothesis Jan18 reviewed Reject Need function for tunable sigmoid 2D surface Jan18 reviewed Close Why integration by part (not partial) is considered everywhere useful? Jan18 reviewed Leave Open How prove this limits $\lim_{n\to\infty}\frac{v_{5}(1^1\cdot 2^2\cdot 3^3\cdot 4^4\cdots\cdot n^n)}{n^2}=\frac{1}{8}$