相关论文: From generalized permutahedra to Grothendieck poly…

We generalize Coincidence theorem due to Walsh for symmetric and linear polynomial in n complex variables, that is linear in each of them having total degre n. We discuss case when total degree is smaller then n. This case has been already…

We give a new method to calculate the universal cohomology classes of coincident root loci. We show a polynomial behavior of them and apply this result to prove that generalized Pl\"ucker formulas are polynomials in the degree, just as the…

In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an example we develop the Heisenberg Lie group…

The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…

A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…

We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the…

Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…

In this paper, we focus on the study of immanantal polynomials for linear combination matrices composed of the degree matrix and adjacency matrix of a graph. First, applying the concept of vertex orientation for general graphs, we provide a…

The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions on the degree of the Forchheimer polynomial are imposed. We derive,…

We construct double Grothendieck polynomials of classical types which are essentially equivalent to but simpler than the polynomials defined by A.N.Kirillov in arXiv:1504.01469 and identify them with the polynomials defined by T.Ikeda and…

We show that the dual character of the flagged Weyl module of any diagram is a positively weighted integer point transform of a generalized permutahedron. In particular, Schubert and key polynomials are positively weighted integer point…

The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…

Gyroscopic alignment of a fluid occurs when flow structures align with the rotation axis. This often gives rise to highly spatially anisotropic columnar structures that in combination with complex domain boundaries pose challenges for…

In this paper, we give a geometrization of semicanonical bases of quantum groups via Grothendieck groups of the derived categories of Lusztig's nilpotent varieties. Meanwhile, we describe the dual semicanonical bases in terms of Serre…

We introduce the sequence of generalized Gon\v{c}arov polynomials, which is a basis for the solutions to the Gon\v{c}arov interpolation problem with respect to a delta operator. Explicitly, a generalized Gon\v{c}arov basis is a sequence…

This paper introduces the notion of complete connectedness of a Grothendieck topos, defined as the existence of a left adjoint to a left adjoint to a left adjoint to the global sections functor, and provides many examples. Typical examples…

In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them…

Pipedreams are combinatorial objects that compute Grothendieck polynomials. We introduce a new combinatorial object that naturally recast the pipedream formula. From this, we obtain the first direct combinatorial formula for the top degree…

For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S^3, such a sequence of polynomials arises naturally as the orders of certain…

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…