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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
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Hottest Questions Today - MathOverflow
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0 days
Often, one deals with objects that can have a certain multiplicity attached to it. In the case of graphs, the multiplicity of vertices connected by an edge gives rise to a hypergraph. Now, in set theory, the axioms are usually stated for sets, and not...
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1 month
On two conditions on a bilinear form over $\mathbf{F}_2$
Let $k$ be a positive integer. Let $n$ and $m$ be positive integers with $m$ roughly $\log_2 n$, let $V$ be an $n$-dimensional vector space over $\mathbb{F}_2$, let $W$ be an $m$-dimensional vector space over $\mathbb{F}_2$, where $\mathbb{F}_2$ is the...
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9 years
Copylefted introduction to topology
Is there a topology textbook with a copyleft license?
Postscript.
You may check my notes now. -
0 days
Some unique coefficients with row sums equal $2$
Let
$T(n,k)$ be an unique coefficients (represented as an irregular triangle) such that for all $n,m \in \mathbb{N}$ we have $$ \sum\limits_{k=1}^{2n} 2^{k-1} \binom{m+k}{k} T(n,k) = (m+2)^{2n} - 1. $$
I conjecture that $$ \sum\limits_{k=1}^{2n} T(n,k) = 2. $$ More precisely, I conjecture that $$ \sum\limits_{k=3}^{2n} T(n,k) = 0. $$ I also conjecture that $T(n,k)$ are integer coefficients for all $1 \leqslant k \leqslant 2n$ iff $2n$ is a power of...
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