Snake-in-the-box code is a Gray code
which can detect single errors.
These codes are important in the context of
rank modulation scheme for representing information
in flash memories. For a Gray code in this
scheme the codewords are permutations, two
consecutive codewords are obtained by using
the "push-to-the-top" operation, and the
distance measure is defined on permutations.
In this paper the Kendall's $tau$-metric is
used as the distance measure.
A recursive construction to obtain a
snake of length $((2n+1)2n-1)M$ for permutations
of $S_{2n+1}$, from a snake of length $M$
for~$S_{2n-1}$, is presented. A direct
construction based on necklaces might
yield snakes of length $frac{(2n+1)!}{2}-2n+1$
for permutations of $S_{2n+1}$.