A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...

In the classification of Fano varieties, those which are not “Gino Fano”, i.e., where −KX is ample but not very ample, are usually annoying. In the beginning of his classification of Fano threefolds, Iskovskikh listed those for which |−KX | is not free. The purpose of this article is to see how his result extends to the canonical Gorenstein case. If X is a Gorenstein Fano threefold with at wors...

This paper contributes to the theory of rational choice under sequential criteria. Following the approach initiated by Manzini and Mariotti (2007) for single-valued choice functions, we characterize choice correspondences that are rational by two sequential criteria under a mild consistency axiom. Rationales ensuring the sequential rationalization are explicitly constructed and a uniquely deter...

We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also allowed to be resonant in the sense that the leading coefficient matrix at each singularity may have arbitrary Jordan canonical form, with a genericity conditi...

With every rational language we associate a canonical non-determinis-tic automaton, that subsumes all possible \minimal" automata recognizing this language.

We show that a refined version of Golyshev’s canonical strip hypothesis does hold for the Hilbert polynomials of complete intersections in rational homogeneous spaces.

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z + 1) + w(z − 1) = R(z, w(z)) (†) where R(z, w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else equation (†) can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painleve eq...

theory of q-difference equations to a comparable degree of completeness. This program includes in particular the complete theory of the convergence and divergence of formal series, the explicit determination of the essential transcendental invariants (constants in the canonical form), the inverse Riemann theory both for the neighborhood of x = o and in the complete plane (case of rational coeff...

Let G be a finitely generated group, and let mn(G) denote the number of maximal subgroups index n. An upper bound is given for degree subgroup growth all polycyclic metabelian groups (i.e., limsup log n, polynomial mn(G)). A condition when this attained. G=Zk⋊AZ, where generator Z on right acts (by conjugation) Zk by multiplication A∈GL(k,Z). It shown that grows like equal to blocks in rational...