I was struggling with this paper about codes which can correct single deletion and re-ranking in permutations, http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6875337
[Published in: Information Theory (ISIT), 2014 IEEE International Symposium on Date of Conference: June 29 2014-July 4 2014, Page(s): 2764 - 2768 INSPEC Accession Number: 14515064, Conference Location : Honolulu, HI DOI: 10.1109/ISIT.2014.6875337 Publisher: IEEE]
- I wonder if there is a longer and more explained version of Theorem 2 in this paper. Or is there any other paper which explains this better?
The "Theorem 2" at the end is extremely difficult to follow!
For example at the top of the second column in page 5 even the authors state things like "it is straightforward (but tedious) to see that the set of possible values for x is exactly $\{u,u+1,..,v+1\}$".
Can someone help understand this?
Many of the things towards the end were not easy to follow : like why is $\{\sigma_i,..,\sigma_j\}$ an increasing run of $\sigma$ and why is $\{p,p+1,..,q\}$ an increasing sub-sequence of $\sigma$.
The above is not looking obvious from the initial definition :
In the beginning the $i$ and $j$ were defined such that from position $i$ to $j$ in the "signature" vector of the permutation $\pi$ is a sequence of $1$s. And $p$ and $q$ were initially defined such that from the position $p$ to $q$ is a sequence of $1$s in the signature vector of the permutation $\pi^{-1}$. And $\sigma$ is a permutation obtained from $\pi$ after a single deletion and re-ranking.
