Christoffel words
E947536
Christoffel words are special finite binary or k-ary words in combinatorics on words that encode discrete approximations of straight lines and have deep connections to number theory, geometry, and Sturmian sequences.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Christoffel words canonical | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
binary word
ⓘ
combinatorial object ⓘ finite word ⓘ k-ary word ⓘ mathematical concept ⓘ |
| alphabet |
finite k-letter alphabet
ⓘ
{0,1} ⓘ |
| appearsIn |
combinatorics on words literature
ⓘ
discrete geometry literature ⓘ symbolic dynamics literature ⓘ |
| characterizedBy |
minimal imbalance between letters
ⓘ
occurring as finite factors of Sturmian words ⓘ slope given by a rational number p/q ⓘ |
| encodes | discrete approximation of straight lines ⓘ |
| field |
combinatorics on words
ⓘ
discrete geometry ⓘ number theory ⓘ symbolic dynamics ⓘ theoretical computer science ⓘ |
| generalizationOf |
lower mechanical words of rational slope
ⓘ
upper mechanical words of rational slope ⓘ |
| hasAspect |
lower Christoffel word
ⓘ
upper Christoffel word ⓘ |
| hasConnectionWith |
Calkin–Wilf tree
NERFINISHED
ⓘ
Christoffel tree NERFINISHED ⓘ Dyck paths (via encodings) ⓘ Euclidean algorithm NERFINISHED ⓘ continued fraction expansion of slopes ⓘ |
| hasProperty |
Lyndon word (for certain orientations)
ⓘ
balanced ⓘ primitive (not a proper power) in typical definitions ⓘ |
| namedAfter | Elwin Bruno Christoffel NERFINISHED ⓘ |
| playsRoleIn |
classification of balanced finite words
ⓘ
geometric representation of Sturmian words ⓘ |
| relatedTo |
Beatty sequences
NERFINISHED
ⓘ
Farey sequences NERFINISHED ⓘ Sturmian sequences NERFINISHED ⓘ Sturmian words ⓘ continued fractions ⓘ discrete lines ⓘ lattice paths ⓘ mechanical words ⓘ |
| studiedSince | 19th century ⓘ |
| usedIn |
analysis of Sturmian morphisms
ⓘ
coding of irrational rotations ⓘ combinatorial number theory ⓘ discrete geometry of digital straight segments ⓘ symbolic codings of lines of rational slope ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.