We say a family of strings over an alphabet is an UMFF if every string has a unique maximal factorization over . Foundational work by Chen, Fox and Lyndon established properties of the Lyndon circ-UMFF, which is based on lexicographic ordering. Commencing with the circ-UMFF related to V-order, we then proved analogous factorization families for a further 32 Block-like binary orders. Here we distinguish between UMFFs and circ-UMFFs, and then study the structural properties of circ-UMFFs. These properties give rise to the complete construction of any circ-UMFF. We prove that any circ-UMFF is a totally ordered set and a factorization over it must be monotonic. We define atom words and initiate a study of u, v-atoms. Applications of circ-UMFFs arise in string algorithmics.
|Nifer y tudalennau||12|
|Cyfnodolyn||International Journal of Foundations of Computer Science|
|Dynodwyr Gwrthrych Digidol (DOIs)|
|Statws||Cyhoeddwyd - 01 Awst 2008|
|Cyhoeddwyd yn allanol||Ie|