6533b823fe1ef96bd127f649
RESEARCH PRODUCT
On the number of factors of Sturmian words
Filippo MignosiFilippo Mignosisubject
Set (abstract data type)Euler functionCombinatoricssymbols.namesakeRiemann hypothesisGeneral Computer ScienceSturmian wordsymbolsComputer Science(all)Theoretical Computer ScienceMathematicsdescription
Abstract We prove that for m ⩾1, card( A m ) = 1+∑ m i =1 ( m − i +1) ϕ ( i ) where A m is the set of factors of length m of all the Sturmian words and ϕ is the Euler function. This result was conjectured by Dulucq and Gouyou-Beauchamps (1987) who proved that this result implies that the language (∪ m ⩾0 A m ) c is inherently ambiguous. We also give a combinatorial version of the Riemann hypothesis.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1991-05-01 | Theoretical Computer Science |