Glossary for combinatorics on words: Difference between revisions

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| size/cardinality of alphabet || arity ||

|-

| word || scale || A finite, right-infinite, or bi-infinite string of letters taken from an alphabet.

| [[word]] || scale || A finite, right-infinite, or bi-infinite string of letters taken from an alphabet.

|-

| conjugate || equivalent under modal rotation || Words ''u'' and ''v'' are conjugate if there exist words ''s'' and ''t'' such that ''u'' = ''st'' and ''v'' = ''ts''. Compare: any two group elements of the form ''st'' and ''ts'' are also conjugate.

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| Parikh vector || interval occurring in a scale || A given subword ''w'' is associated with a ''Parikh vector'' whose coefficient for each letter ''a'' is |''w''|<sub>''a''</sub>, the number of occurrences of ''a'' in ''w''. The Parikh vector of a length-''k'' subword is a ''k''-step in xen terminology.

|-

| (1-)~~balanced~~ word || (for binary words) MOS scale || A word such that for any ''k'' and any two ''k''-steps, the numbers of occurrences of any letter differ by at most 1.

| (1-)[[balance]]d word || (for binary words) MOS scale || A word such that for any ''k'' and any two ''k''-steps, the numbers of occurrences of any letter differ by at most 1.

|}

@@ Line 12: / Line 12: @@
 | size/cardinality of alphabet || arity ||
 |-
-| word || scale || A finite, right-infinite, or bi-infinite string of letters taken from an alphabet.
+| [[word]] || scale || A finite, right-infinite, or bi-infinite string of letters taken from an alphabet.
 |-
 | conjugate || equivalent under modal rotation || Words ''u'' and ''v'' are conjugate if there exist words ''s'' and ''t'' such that ''u'' = ''st'' and ''v'' = ''ts''. Compare: any two group elements of the form ''st'' and ''ts'' are also conjugate.
@@ Line 44: / Line 44: @@
 | Parikh vector || interval occurring in a scale || A given subword ''w'' is associated with a ''Parikh vector'' whose coefficient for each letter ''a'' is &#124;''w''&#124;<sub>''a''</sub>, the number of occurrences of ''a'' in ''w''. The Parikh vector of a length-''k'' subword is a ''k''-step in xen terminology.
 |-
-| (1-)balanced word || (for binary words) MOS scale || A word such that for any ''k'' and any two ''k''-steps, the numbers of occurrences of any letter differ by at most 1.
+| (1-)[[balance]]d word || (for binary words) MOS scale || A word such that for any ''k'' and any two ''k''-steps, the numbers of occurrences of any letter differ by at most 1.
 |}