What is the maximum weighted earth-mover's distance (as defined in [Sun et. al. 2010][1]) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words

[![enter image description here][2]][2]

Is it

 $$(n-1)w_1 + (n-2) w_2 + \cdots + w_{n-1}$$


for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?

Apologies if this is a very obvious question!


  [1]:http://theanalysisofdata.com/gl/searchEngineVis.pdf
  [2]: https://i.sstatic.net/vG3mq.png