A word on a nite alphabet A is said to be overlap free if it contains no factor of the form xuxux where x is a letter and u a possibly empty word In this paper we study the number un of overlap free binary words of length n which is known to be bounded by a polynomial in n First we describe a bijection between the set of overlap free words and a rational language This yields recurrence relation...

Motivated by recent results in mathematical virology, we present novel asymmetric Z[τ]-integer-valued affine extensions of the non-crystallographic Coxeter groups H2, H3 and H4 derived in a Kac-Moody-type formalism. In particular, we show that the affine reflection planes which extend the Coxeter group H3 generate (twist) translations along 2-, 3and 5-fold axes of icosahedral symmetry, and we c...

Let P(Σ∗) be the semiring of languages, and consider its subset P(Σ). In this paper we define the language recognized by a weighted automaton over P(Σ) and a one-letter alphabet. Similarly, we introduce the notion of language recognition by linear recurrence equations with coefficients in P(Σ). As we will see, these two definitions coincide. We prove that the languages recognized by linear recu...

Chomsky and Schützenberger showed in 1963 that the sequence dL(n), which counts the number of words of a given length n in a regular language L, satisfies a linear recurrence relation with constant coefficients for n, i.e., it is C-finite. It follows that every sequence s(n) which satisfies a linear recurrence relation with constant coefficients can be represented as dL1 (n)− dL2 (n) for two re...

A random vector X with representation X = ∑ j≥0 AjZj is considered. Here, (Zj) is a sequence of independent and identically distributed random vectors and (Aj) is a sequence of random matrices, ‘predictable’ with respect to the sequence (Zj). The distribution of Z1 is assumed to be multivariate regular varying. Moment conditions on the matrices (Aj) are determined under which the distribution o...

We show that the commutative closure of a star-free language is either star-free or not regular anymore. Actually, this property is shown to hold exactly for the closure with respect to a partial commutation corresponding to a transitive dependence relation. Moreover, the question whether the closure of a star-free language remains star-free is decidable precisely for transitive partial commuta...

Let φ : X → Y be a generically finite morphism. The purpose of this paper is to show how the OY -algebra structure on φ∗OX controls algebro-geometric aspects of X like the ring generation of graded rings associated to X and the very ampleness of line bundles on X . As the main application of this we prove some new results for certain regular surfaces X of general type. Precisely, we find the de...