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Apr
1
comment Numbers of distinct products obtained by permuting the factors
What about generalizing the problem: given any equivalence relation on $S_n$, can one find $G$ and the $g_i$ such that the map $S_n\to G,\: \sigma \mapsto g_{\sigma(1)}\cdot\ldots\cdot g_{\sigma(n)}$ identifies two permutations if and only if they are equivalent? Or is this trivially false?
Mar
25
awarded  Suffrage
Feb
28
comment Does every separated measurable space embed into a power of $\{0,1\}$?
That's precisely what I had tried initially (see the original version of my question). If you know about Gelfand duality and Stone duality, it seems like a natural thing to try and indeed the resulting injective function is measurable (with respect to the Baire, and hence also the Borel $\sigma$-algebra on $\{0,1\}^\Sigma$). However, I don't see why this function should also take measurable sets to measurable sets, and I think this fails in general. In fact, I suspect that its image may not even be measurable, but I don't have a concrete example of that.
Feb
28
accepted Does every separated measurable space embed into a power of $\{0,1\}$?
Feb
28
comment Does every separated measurable space embed into a power of $\{0,1\}$?
Neat answer! I can't accept both, so I will go with Joseph's which covers the Borel case, since it also contains a sufficient condition which is close to his necessary one.
Feb
27
comment Does every separated measurable space embed into a power of $\{0,1\}$?
@Joseph: I updated the question to reflect your correction. A more detailed answer would be great!
Feb
27
revised Does every separated measurable space embed into a power of $\{0,1\}$?
added 838 characters in body
Feb
27
comment Does every separated measurable space embed into a power of $\{0,1\}$?
@Joseph: you're right. I will have to think about it a bit more. Sorry for the confusion...
Feb
27
revised Does every separated measurable space embed into a power of $\{0,1\}$?
clarified the question after a request in the comments
Feb
27
comment Does every separated measurable space embed into a power of $\{0,1\}$?
@Joel: yes, that's exactly what I mean. I'll clarify the question accordingly.
Feb
27
revised Does every separated measurable space embed into a power of $\{0,1\}$?
deleted 132 characters in body
Feb
27
asked Does every separated measurable space embed into a power of $\{0,1\}$?
Feb
14
awarded  Scholar
Feb
14
accepted graphs with independence number = Shannon capacity
Feb
14
answered graphs with independence number = Shannon capacity
Jan
29
comment Resource for learning quantum mechanics from the viewpoint of representation theory
Maybe this should be Community Wiki?
Jan
29
answered Resource for learning quantum mechanics from the viewpoint of representation theory
Jan
11
comment graphs with independence number = Shannon capacity
@Graphth and everybody else: we have finally disproved all these conjectures and are currently in the process of revising our manuscript accordingly. The proof is somewhat indirect and actually does make use of the relationship to quantum information theory that we develop. I will compose a more detailed answer as soon as the updated manuscript is on the arXiv.
Nov
20
revised Replacing commutative C*-algebras by simple ones
added missing tag
Nov
19
suggested suggested edit on Replacing commutative C*-algebras by simple ones