Glossary for combinatorics on words: Difference between revisions

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| alphabet || || A countable set of symbols.
| alphabet || || A countable set of symbols.
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| word || scale || A finite, or infinite string of letters taken from an alphabet.
| word || scale || A finite or infinite string of letters taken from an alphabet.
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| circular word || [[periodic scale]] || An equivalence class of words that are modally equivalent, or equivalently, an infinite periodic word.
| circular word || [[periodic scale]] || An equivalence class of words that are modally equivalent, or equivalently, an infinite periodic word.

Revision as of 15:59, 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 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.