Glossary for combinatorics on words: Difference between revisions
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! Standard term(s) !! Xen term(s) !! Definition | ! Standard term(s) !! Xen term(s) !! Definition | ||
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| alphabet || || A countable set of symbols. | | alphabet || abstract steps || A countable set of symbols. | ||
|- | |- | ||
| word || scale || A finite or infinite string of letters taken from an alphabet. | | word || abstract 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. | | circular word || [[periodic scale]] || An equivalence class of words that are modally equivalent, or equivalently, an infinite periodic word. | ||
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| abelian complexity || [[interval variety|variety]] of an [[interval class]] || | | abelian complexity || [[interval variety|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>. | | 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''|<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. | | (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. | ||
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Revision as of 16:09, 4 November 2023
This page collects definitions and xen community equivalents of standard terminology used in combinatorics on words.
| Standard 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. |
| circular word | periodic scale | An equivalence class of words that are modally equivalent, 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 | |
| Sturmian word | aperiodic MOS scale | |
| cutting word | 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. |