  In this paper we develop a theory describing how the extended Burrows-Wheeler
Transform (eBWT) of a collection of DNA fragments tends to cluster together the
copies of nucleotides sequenced from a genome G. Our theory accurately predicts
how many copies of any nucleotide are expected inside each such cluster, and
how an elegant and precise LCP array based procedure can locate these clusters
in the eBWT. Our findings are very general and can be applied to a wide range
of different problems. In this paper, we consider the case of alignment-free
and reference-free SNPs discovery in multiple collections of reads. We note
that, in accordance with our theoretical results, SNPs are clustered in the
eBWT of the reads collection, and we develop a tool finding SNPs with a simple
scan of the eBWT and LCP arrays. Preliminary results show that our method
requires much less coverage than state-of-the-art tools while drastically
improving precision and sensitivity.
