6533b854fe1ef96bd12af679
RESEARCH PRODUCT
On the product of balanced sequences
Antonio RestivoGiovanna Rosonesubject
SequenceGeneral MathematicsSturmian wordPeriodic sequenceBinary numberbalanceSturmian wordsInfinite sequences; Sturmian words; balanceComputer Science ApplicationsCombinatoricsInfinite sequencesSection (category theory)Product (mathematics)Infinite sequenceproductAlphabetSoftwareMathematicsdescription
The product w = u ⊗ v of two sequences u and v is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product w of two balanced sequences u,v is balanced too. In the case u and v are binary sequences, we prove, as a main result, that, if such a product w is balanced and deg ( w ) = 4, then w is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems proposed show the interest of the notion of product in the study of balanced sequences.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-14 |