Glossary for combinatorics on words: Difference between revisions

Revision as of 15:56, 4 November 2023

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

Definitions
Standard term(s)	Xen term(s)	Definition
alphabet		A countable set of symbols.
word	scale	A finite, or infinite string of letters taken from an alphabet.
circular word	periodic scale	An equivalence class of words that are modally equivalent, or equivalently, an infinite periodic word.
subword, factor		u is a subword of w if w = yuv for words y and v.
Christoffel word	brightest mode of a periodic MOS scale
Sturmian word	aperiodic MOS scale
cutting word	billiard scale
abelian complexity	variety of an interval class
Parikh vector	interval	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.

@@ Line 1: / Line 1: @@
 This page collects definitions and xen community equivalents of standard terminology used in combinatorics on words.
+{| class="wikitable sortable"
+|+ Definitions
+|-
+! Standard term(s) !! Xen term(s) !! Definition
+|-
+| alphabet || || A countable set of symbols.
+|-
+| word || scale || A finite, or infinite string of letters taken from an alphabet.
+|-
+| circular word || [[periodic scale]] || An equivalence class of words that are modally equivalent, or equivalently, an infinite periodic word.
+|-
+| subword, factor || || u is a subword of w if w = yuv for words y and v.
+|-
+| Christoffel word || brightest mode of a periodic MOS scale ||
+|-
+| Sturmian word || aperiodic MOS scale ||
+|-
+| cutting word || [[billiard scale]] ||
+|-
+| abelian complexity || [[variety]] of an [[interval class]] ||
+|-
+| Parikh vector || interval || A given subword ''w'' is associated with a ''Parikh vector'' whose coefficient for each letter ''a'' is |''w''|<sub>''a''</sub>.
+|-
+| (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.
+|}