Glossary for combinatorics on words: Difference between revisions

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 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.
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+| Christoffel word || brightest mode of a periodic MOS scale ||
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+| Sturmian word || aperiodic MOS scale ||
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+| cutting word || [[billiard scale]] ||
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+| abelian complexity || [[variety]] of an [[interval class]] ||
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+| Parikh vector || interval || A given subword ''w'' is associated with a ''Parikh vector'' whose coefficient for each letter ''a'' is |''w''|<sub>''a''</sub>.
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+| (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.
+|}