Balancing and clustering of words in the Burrows-Wheeler transform
Theoretical Computer Science
Two combinatorial criteria for BWT images
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
| Hi-index | 0.00 |
The investigation of the "clustering effect" of the Burrows-Wheeler transform (BWT) leads to study the words having simple BWT, i.e. words w over an ordered alphabet A = {a 1,a 2,...,a k }, with a 1 a 2 a k , such that bwt(w) is of the form $a_k^{n_k} a_{k-1}^{n_{k-1}} \cdots a_1^{n_1}$, for some non-negative integers n 1, n 2, ..., n k . We remark that, in the case of binary alphabets, there is an equivalence between words having simple BWT, the family of (circular) balanced words and the conjugates of standard words. In the case of alphabets of size greater than two, there is no more equivalence between these notions. As a main result of this paper we prove that, under assumption of balancing, the following three conditions on a word w are equivalent: i) w has simple BWT, ii) w is a circularly rich word, and iii) w is a conjugate of a finite epistandard word.