Related papers: Residues of skew rational functions

We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.

The plethysm product of Schur functions corresponds to composing polynomial representations of infinite general linear groups. Finding the plethysm coefficients $\langle s_\nu \circ s_\mu, s_\lambda\rangle$ that express an arbitrary…

We give new product formulas for the number of standard Young tableaux of certain skew shapes and for the principal evaluation of the certain Schubert polynomials. These are proved by utilizing symmetries for evaluations of factorial Schur…

We put together the ingredients for an efficient operator calculus based on Krawtchouk polynomials, including Krawtchouk transforms and corresponding convolution structure which provide an inherently discrete alternative to Fourier…

Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and…

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders.…

Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…

Subresultant of two univariate polynomials is a fundamental object in computational algebra and geometry with many applications (for instance, parametric GCD and parametric multiplicity of roots). In this paper, we generalize the theory of…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant.…

We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies…

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function…

Let $k$ and $m$ be positive integers and $\lambda/\mu$ a skew partition. We compute the principal specialization of the skew Schur polynomials $s_{\lambda /\mu}(x_1, \ldots, x_{k})$ modulo $q^m-1$ under suitable conditions. We interpret the…

Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current…

The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…

We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic…

We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance between two tuples of matrices is captured by a weight…