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Feb 21, 2019 at 6:59 vote accept Taras Banakh
Feb 21, 2019 at 4:41 answer added James timeline score: 1
Feb 2, 2019 at 8:53 history edited Taras Banakh
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Feb 1, 2019 at 23:01 comment added YCor As I said, this reduces to a question with no reference to the symmetric difference and hence no group theory. It's a combinatorial optimization problem. I would rephrase more concisely the question in this way (and tag combinatorial-optimization) to hope for optimal feedback: "Let $X$ be a finite set of finite even cardinal. For every metric $d$ on $X$, define $L(d)$ as (...). How to compute $L(d)$?"
Feb 1, 2019 at 22:11 history edited Taras Banakh CC BY-SA 4.0
edited body
Feb 1, 2019 at 19:20 comment added YCor Just to streamline notation, you have $\hat{d}(A,B)=\ell(A\oplus B)$, where you can call $\ell(A)=\hat{d}(\emptyset,A)$ the Graev length of $A$. The question is about computing $\ell(A)$.
Feb 1, 2019 at 19:17 history edited YCor CC BY-SA 4.0
fixed typo in title
Feb 1, 2019 at 19:14 history asked Taras Banakh CC BY-SA 4.0