Glossary for combinatorics on words

This page collects definitions and xen community equivalents of standard academic terminology used in combinatorics on words.

(Scales are understood to be abstract with equaves unspecified.)

Definitions

Academic term(s)	Xen term(s)	Definition
alphabet	steps	A countable set of symbols called letters.
word	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.