相关论文: Algebraic aspects of increasing subsequences

The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical…

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width-$k$ descents and width-$k$ inversions. These variations induce generalizations of the excedance and major statistics,…

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…

In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of…

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…

In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional…

In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential equations, in particular for the class of fractional abstract…

A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…

We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…

We introduce an algebra model to study higher order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum…

This paper presents some new Lie groups preserving fixed subspaces of geometric algebras (or Clifford algebras) under the twisted adjoint representation. We consider the cases of subspaces of fixed grades and subspaces determined by the…

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…

We present a partial generalization to Schubert calculus on flag varieties of the classical Littlewood-Richardson rule, in its version based on Schuetzenberger's jeu de taquin. More precisely, we describe certain structure constants…

We give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then us this to provide a new bound on trilinear and quadrilinear…

We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_b(\mathbb{R}^d;\mathbb{R}^m)$ of bounded and continuous functions, associated to a class of nonautonomous weakly coupled…