To prove that a pattern p is avoidable on a given alphabet, one has to construct an innnite language L that avoids p. Usually, L is a DOL-language (obtained by iterating a morphism h) or a HDOL-language (obtained by coding a DOL-language with another morphism g). Our purpose is to nd an algorithm to test, given a HDOL-system G, whether the language L(G) generated by this system avoids p. We rst...

Morphisms to finite semigroups can be used for recognizing omega-regular languages. The socalled strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphi...

We introduce signed exceptional sequences as factorizations of morphisms in the cluster morphism category. The objects of this category are wide subcategories of the module category of a hereditary algebra. A morphism [T ] : A → B is an equivalence class of rigid objects T in the cluster category of A so that B is the right hom-ext perpendicular category of the underlying object |T | ∈ A. Facto...

If, for a morphism σ : ∆∗ → Σ∗ (where ∆ and Σ are arbitrary alphabets) and a word α ∈ ∆∗, there exists another morphism τ mapping α to σ(α), then σ is called ambiguous with respect to α ; if such a τ does not exist, then σ is unambiguous. For example, the morphism σ0 : {A,B,C}∗ → {a,b}∗ – given by σ0(A) := a, σ0(B) := a, σ0(C) := b – is ambiguous with respect to the word α0 := ABCACB, since the...

We give a characterization of all the sets X such that any morphism h on fa; bg is overlap-free ii for all x in X , h(x) is overlap-free. As a consequence, we observe the particular case X = fbbabaag which improves the previous characterization of Berstel-S e ebold 2]. R esum e Nous donnons une caract erisation de tous les ensembles X tels qu'un morphisme h sur fa; bg est sans chevauchement si ...

Let K be a discrete valuation field with ring of integers OK . Let f :X → Y be a finite morphism of curves overK . In this article, we study some possible relationships between the models over OK of X and of Y . Three such relationships are listed below. Consider a Galois cover f :X→ Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-st...

Hitchin [Duke Math. J. 54(1), 91–114 (1987)] introduced a proper morphism from the moduli space of stable G-Higgs bundles [[Formula: see text] and [Formula: text]] over curve to vector invariant polynomials, he described generic fibers that morphism. In this paper, we first describe for parabolic projective symplectic/orthogonal Higgs without fixing determinant. We also when determinant is triv...

In this article we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] the authors establish an isomorphism between Hamiltonian Floer homology and singular homology of the underlying symplectic manifold. In general, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian su...

This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct images. Some results are new.