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The block sorting lossless data compression algorithm (BSLDCA) described by Burrows and Wheeler (1994) has received considerable attention. It achieves as good compression rates as context-based methods, such as PPM, but at execution speeds closer to Ziv-Lempel techniques. This paper, describes the lexical permutation sorting algorithm (LPSA), its theoretical basis, and delineates its relationship to the BSLDCA. In particular we describe how the BSLDCA can be reduced to the LPSA and show how the LPSA could give better results than the BSLDCA when transmitting permutations. We also introduce a new technique, inversion frequencies, and show that it does as well as move-to-front (MTF) coding when there is locality of reference in the data.