Glossary for combinatorics on words
This page collects definitions and xen community equivalents of standard academic terminology used in combinatorics on words.
(Equaves are always unspecified.)
| Academic term(s) | Xen term(s) | Definition |
|---|---|---|
| alphabet | abstract steps | A countable set of symbols. |
| word | abstract scale | A finite or infinite string of letters taken from an alphabet. |
| conjugate | equivalent under modal rotation | |
| circular word | periodic scale | An equivalence class of words that are conjugate, or equivalently, an infinite periodic word. |
| factor, subword | u is a factor of w if w = yuv for words y and v. | |
| Christoffel word | brightest mode of a periodic MOS scale | |
| Lyndon word | lexicographically brightest mode | A word that is lexicographically first among its rotations |
| Sturmian word | aperiodic MOS scale | |
| cutting word, cutting sequence | billiard scale | |
| abelian complexity | variety of an interval class | |
| Parikh vector | interval; the Parikh vector of a length-k subword is a k-step. | A given subword w is associated with a Parikh vector whose coefficient for each letter a is |w|a. |
| (1-)balanced word | (for binary words) MOS scale | A word such that for any k, the number of occurrences of any letter in any two k-steps differ by at most 1. |