  Local rank modulation scheme was suggested recently for representing
information in flash memories in order to overcome drawbacks of rank
modulation. For $0 < s\leq t\leq n$ with $s$ divides $n$, an $(s,t,n)$-LRM
scheme is a local rank modulation scheme where the $n$ cells are locally viewed
cyclically through a sliding window of size $t$ resulting in a sequence of
small permutations which requires less comparisons and less distinct values.
The gap between two such windows equals to $s$. In this work, encoding,
decoding, and asymptotic enumeration of the $(1,3,n)$-LRM scheme is studied.
The techniques which are suggested have some generalizations for $(1,t,n)$-LRM,
$t > 3$, but the proofs will become more complicated. The enumeration problem
is presented also as a purely combinatorial problem. Finally, we prove the
conjecture that the size of a constant weight $(1,2,n)$-LRM Gray code with
weight two is at most $2n$.
