On the Number of Rich Words
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00316065" target="_blank" >RIV/68407700:21340/17:00316065 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/chapter/10.1007%2F978-3-319-62809-7_26" target="_blank" >https://link.springer.com/chapter/10.1007%2F978-3-319-62809-7_26</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-62809-7_26" target="_blank" >10.1007/978-3-319-62809-7_26</a>
Alternative languages
Result language
angličtina
Original language name
On the Number of Rich Words
Original language description
Any finite word $w$ of length $n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is reached, the word $w$ is called rich. The number of rich words of length $n$ over an alphabet of cardinality $q$ is denoted $R_q(n)$. For binary alphabet, Rubinchik and Shur deduced that ${R_2(n)}leq c 1.605^n $ for some constant $c$. In addition, Guo, Shallit and Shur conjectured that the number of rich words grows slightly slower than $n^{sqrt{n}}$. We prove that $limlimits_{nrightarrow infty }sqrt[n]{R_q(n)}=1$ for any $q$, i.e. $R_q(n)$ has a subexponential growth on any alphabet.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Developments in Language Theory
ISBN
978-3-319-62809-7
ISSN
1611-3349
e-ISSN
—
Number of pages
8
Pages from-to
345-352
Publisher name
Springer, Cham
Place of publication
—
Event location
Liège, Belgium
Event date
Aug 7, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—