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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
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