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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
Mathoverflow.net news digest
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0 days
Proving a sum of binomials and harmonic numbers identity
I am trying to prove a complex identity involving harmonic numbers $H_n$ and generalized harmonic numbers $H^{(2)}_n$.
For integers $m, a, b, c$ such that $c \ge 0$ and $c \le \min\left(\lfloor \frac{2m-b-1}{2} \rfloor, m-a-1\right)$, let us define the weight term:$$ W_k = \frac{(-1)^{3m-a-b+k}}{(2m-b-1-2k)! (m-a-k-1)! (k!)^3} $$... -
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Qiaochu Yuan recently tweeted the following analogy:
the sense in which prime numbers are the building blocks of other numbers (wrt multiplication) is exactly analogous to the sense in which connected graphs are the building blocks of arbitrary graphs. an arbitrary graph, not necessarily connected, consists... -
0 days
Reference for congruences in $\mathbf{Rel}$
In CatDat we are currently working out the proof that $\mathbf{Rel}$ has quotients of congruences. Apparently this cannot be deduced from general results, for example $\mathbf{Rel}$ does not have reflexive coequalizers. Daniel Schepler has found a proof...
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0 days
Spectral geometry: is this a typo in Alberto Arabia's "Introduction to Isospectr...
My advisor and I are doing a project on spectral geometry. To get the necessary prerequisites down, I am consulting Alberto Arabia's Introduction to Isospectrality. Theorem 1.2.2 in this book reads as follows:
Let $\mathbf M$ be a PLB-surface. Let $(G,\Gamma_1,\Gamma_2)$ be a Gassman triple where $G$ is a finite subgroup of $\operatorname{Iso}(\mathbf M)$ and where the subgroups $\Gamma_i$ act freely on $\mathbf M$. Then, the quotients $\mathbf M_i:=\Gamma...
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