Glossary for combinatorics on words: Difference between revisions

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! Standard term(s) !! Xen term(s) !! Definition

|-

| 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.

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| abelian complexity || [[interval variety|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>.

| 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.

|}

@@ Line 6: / Line 6: @@
 ! Standard term(s) !! Xen term(s) !! Definition
 |-
-| 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.
@@ Line 22: / Line 22: @@
 | abelian complexity || [[interval variety|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 &#124;''w''&#124;<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 &#124;''w''&#124;<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.
 |}