Shortlex order

In mathematics, and particularly in the theory of automatic groups, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences are primarily sorted by cardinality (length) with the shortest sequences first, and sequences of the same length are sorted into lexicographical order. Shortlex ordering is also called radix, or length-plus-lexicographic ordering.

References

• Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio V. F.; Paterson, Michael S.; Thurston, William P. (1992), Word processing in groups, Boston, MA: Jones and Bartlett Publishers, p. 56, ISBN 0-86720-244-0, MR 1161694 .