zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On critical exponents in fixed points of non-erasing morphisms. (English) Zbl 1227.68074
Ibarra, Oscar H. (ed.) et al., Developments in language theory. 10th international conference, DLT 2006, Santa Barbara, CA, USA, June 26--29, 2006. Proceedings. Berlin: Springer (ISBN 3-540-35428-X/pbk). Lecture Notes in Computer Science 4036, 280-291 (2006).
Let $\Sigma $ be an alphabet of size $t$, let $f: \Sigma ^{*}\rightarrow \Sigma ^{*}$ be a non-erasing morphism, let $w$ be an infinite fixed point of $f$, and let $E(w)$ be the critical exponent of $w$. We prove that if $E(w)$ is finite, then for a uniform $f$ it is rational, and for a non-uniform $f$ it lies in the field extension ${{\mathbb Q}[{\lambda_1},\ldots,{\lambda_\ell}]}$, where $\lambda _{1},\dots ,\lambda _{\ell }$ are the eigenvalues of the incidence matrix of $f$. In particular, $E(w)$ is algebraic of degree at most $t$. Under certain conditions, our proof implies an algorithm for computing $E(w)$. For the entire collection see [Zbl 1108.68001].
68Q70Algebraic theory of languages and automata
68R15Combinatorics on words
Full Text: DOI