Burrows Wheeler Transformation - Transformation Vector

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After transforming the input text of "abracdabra!", my transformation vector is [3, 0, 5, 6, 7, 9, 10, 8, 2, 1, 4], the text is then piped through a few more transformations and compressed to disk.

After closing the program, we obviously no longer have access to the transformation vector. Are we expected to write the transformation vector to disk? Wouldn't the size of the vector actually equal n characters? Wouldn't this actually increase the size of the compressed file?

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The Burrows Wheeler Transformation is reversible without the transformation vector.