Related papers: An Example of Pi^0_3-complete Infinitary Rational …
For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative completion of the free algebra is the free completely…
We introduce a novel technique to analyse unambiguous B\"uchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant…
In this paper, a question due to Heckenberger, Shareshian and Welker on racks in [7] is positively answered. A rack is a set together with a selfdistributive bijective binary operation. We show that the lattice of subracks of every finite…
In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
A finite family of $R_I$ polynomials is introduced and studied. It consists in a set of polynomials of $_{3}F_{2}$ form whose biorthogonality to an ensemble of rational functions is spelled out. These polynomials are shown to satisfy two…
Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures is complete for $\Sigma^1_1$; the first…
In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite…
Suppose $Y$ is a compact, connected, oriented 3-manifold possibly with boundary, such that $\pi_1(Y)$ is infinite. Let $\operatorname{Diff}_\partial(I\times Y)$ denote the group of self-diffeomorphisms of $I\times Y$ that are equal to the…
We show that the $n$'th digit of the base-$b$ representation of the golden ratio is a finite-state function of the Zeckendorf representation of $b^n$, and hence can be computed by a finite automaton. Similar results can be proven for any…
Much work has been done to study groups with few rational conjugacy classes or few rational irreducible characters. In this paper we look at the opposite extreme. Let $G$ be a finite group. Given a conjugacy class $K$ of $G$, we say it is…
We study aleph_0-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of lambda-Borel completeness and prove that such theories are…
If $G$ is a finite group, an irreducible complex-valued character $\chi$ is called rational if $\chi(g)$ is rational for all $g\in G$. Also, a conjugacy class $x^G$ is called rational, if for all irreducible complex-valued character $\chi$,…
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
We follow a connection between tight determinisation and complementation and establish a complementation procedure from parity automata to nondeterministic B\"uchi automata and prove it to be tight up to an $O(n)$ factor, where $n$ is the…
We introduce partially ordered two-way B\"uchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way B\"uchi automata are B\"uchi automata which can change the direction…
We compare crystal combinatorics of the level $2$ Fock space with the classification of unitary representations of type $B$ rational Cherednik algebras to show that any finite-dimensional unitary irreducible representation of such an…
It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…
Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the B\"uchi and Muller ones [1]. It was proved…
We prove that the category $\mathsf{SBor}$ of standard Borel spaces is the (bi-)initial object in the 2-category of countably complete Boolean (countably) extensive categories. This means that $\mathsf{SBor}$ is the universal category…