  In this paper we present an algorithm to compute the Lyndon array of a string
$T$ of length $n$ as a byproduct of the inversion of the Burrows-Wheeler
transform of $T$. Our algorithm runs in linear time using only a stack in
addition to the data structures used for Burrows-Wheeler inversion. We compare
our algorithm with two other linear-time algorithms for Lyndon array
construction and show that computing the Burrows-Wheeler transform and then
constructing the Lyndon array is competitive compared to the known approaches.
We also propose a new balanced parenthesis representation for the Lyndon array
that uses $2n+o(n)$ bits of space and supports constant time access. This
representation can be built in linear time using $O(n)$ words of space, or in
$O(n\log n/\log\log n)$ time using asymptotically the same space as $T$.
