What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-3} + 2w_{n-2} + w_{n-1}$$$$(n-1)w_1 + (n-2) w_2 + \cdots + w_{n-1}$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-3} + 2w_{n-2} + w_{n-1}$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
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!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-2} + 2w_{n-1} + w_n$$$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-3} + 2w_{n-2} + w_{n-1}$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-2} + 2w_{n-1} + w_n$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-3} + 2w_{n-2} + w_{n-1}$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-2} + 2w_{n-1} + w_n$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010 between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-2} + 2w_{n-1} + w_n$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
What is the maximum weighted earth-mover's distance (as defined in Sun et. al. 2010) between two permutations in $\mathfrak S_n$ where the transposition $(i, i+1)$ has cost given by weight $w_i$. In other words
Is it
$$w_1 + 2w_2 + 3w_3 + \cdots + 3w_{n-2} + 2w_{n-1} + w_n$$
for the permuations $(12\cdots n)$ and $(n(n-1)\cdots 1)$?
Apologies if this is a very obvious question!
