Rank weights of coins with a balance scale
I want to generalized above problem into $n$ coins.
i.e.,
using balance scale, sort $n$ coins in order.
Slightly more generalizing the above post, [In that post, they didn't consider equal weight case] Let's consider, when we balance scale, there are three possibilities. [Let a,b the two coins, then a=b, a>b, a
Making trees for $n=5$, I obtain the number of weighting is 7.
And by the similar computation [with more effort] I figure out for $n=6$, 10 is enough.
How about its generalization to $n$?
At this moment I have no idea how to generalize for $n$.
In searching internet, I found one particular arXiv,
1409.0250, but in there analysis is not matched even in $n=5$. [For example, I thought the section 4 of that paper is the same case with mine, but it seems not...]