OFFSET
1,2
COMMENTS
The Kamae-Xue measure of a word is the sum of the squares of the number of occurrences of each distinct factor (contiguous subword) of w.
LINKS
Teturo Kamae and Yu-Mei Xue, An Easy Criterion for Randomness, Sankhya: The Indian Journal of Statistics, 2015, Volume 77-A, Part 1, pp. 126-152, DOI:10.1007/s13171-014-0054-3.
Teturo Kamae and Dong Han Kim, A characterization of eventual periodicity, Theoretical Computer Science 581 (2015) 1-8, doi:10.1016/j.tcs.2015.02.039.
EXAMPLE
Examples of strings achieving this minimum are 0, 01, 010, 0110, 00110, 001101, 0011010, 01001110, 011100010, 0101110001, 01011100010, 010111000110.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Nov 21 2015
STATUS
approved