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MathOverflow : Recent Questions and Answers (Page 11)

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What is the generic poset used in forcing, really?

I'm not a set theorist, but I understand the 'pop' version of set-theoretic forcing: in analogy with algebra, we can take a model of a set theory, and an 'indeterminate'...

Asked on 12/01/2021

5 answer

Showing block diagonal structure of matrix by reordering

Suppose we have a block-diagonal matrix $M$, but the block diagonal structure is not immediately apparent from looking at the matrix because the rows/columns are shuffled. I wish to find...

Asked on 12/01/2021 by Szabolcs Horvát

6 answer

A new cardinality living in every forcing extension?

I'm broadly interested in notions of "generic presentability" - when a given object exists in every forcing extension of the universe by some fixed forcing, at least up to the...

Asked on 12/01/2021

1 answer

What is the Schur multiplier of the Mathieu group $M_{10}$

It is well known that the automorphism group of the alternating group $A_6$ is $PGamma L_2(9)$. There are three different index $2$ subgroups of $PGamma L_2(9)$,...

Asked on 12/01/2021 by Jiyong Chen

1 answer

Reference describing supersingular elliptic curves over algebraically closed field in characteristic 2

I'm looking for a reference for the fact that over an algebraically closed field of characteristic two, there is (essentially) only one supersingular elliptic curve. This fact appears on Wikipedia,...

Asked on 12/01/2021 by up-too-high

2 answer

Approximation in fractional Sobolev space

Assume $Omegasubset Bbb R^d$ is Lipschitz open set. Let $pgeq 1$ and $0<sleq 1/p$. How to prove that $C_c^infty(Omega)$ is dense in $W^{s,p}(Omega)$? Recall that,...

Asked on 12/01/2021 by Guy Fsone

0 answer

Is the following generalization of the Caratheodory theorem true?

The colorful Carathéodory theorem (Bárány, 1982) considers $d+1$ "colors" $X_1,ldots,X_{d+1}subseteq mathbb{R}^d$, and a point $x$ in the convex hull of each color ($xin text{conv}(X_i)$ for each...

Asked on 12/01/2021

1 answer

Dense embeddings into Euclidean space

The question is a follow-up on this old post. Fix a positive integer $d$ and consider $mathbb{R}^d$ with its usual Euclidean topology. Given a metric...

Asked on 12/01/2021

0 answer

Why did Robertson and Seymour call their breakthrough result a "red herring"?

One of the major results in graph theory is the graph structure theorem from Robertson and Seymourhttps://en.wikipedia.org/wiki/Graph_structure_theorem. It gives a deep and fundamental connection between the theory...

Asked on 12/01/2021 by GraphX

2 answer

The edge precoloring extension problem for complete graphs

Consider coloring the edges of a complete graph on even order. This can be seen as the completion of an order $n$ symmetric Latin square except the leading diagonal....

Asked on 12/01/2021

2 answer

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