相关论文: On parameter spaces for artin level algebras

The polynomial ring $B$ in infinitely many indeterminates $(x_1,x_2,\ldots)$, with rational coefficients, has a vector space basis of Schur polynomials, parametrized by partitions. The goal of this note is to provide an explanation of the…

Given a Schubert class on $Gr(k,V)$ where $V$ is a symplectic vector space of dimension $2n$, we consider its restriction to the symplectic Grassmannian $SpGr(k,V)$ of isotropic subspaces. Pragacz gave tableau formulae for positively…

We completely classify Cartan subalgebras of dimension drop algebras with coprime parameters. More generally, we classify Cartan subalgebras of arbitrary stabilised dimension drop algebras that are non-degenerate in the sense that the…

We pose and solve the equivalence problem for subspaces of ${\mathcal P}_n$, the $(n+1)$ dimensional vector space of univariate polynomials of degree $\leq n$. The group of interest is ${\rm SL}_2$ acting by projective transformations on…

We study a graded vector space of polynomials associated to a square matrix, defined by a finite difference condition along the rows. We show this space coincides with one defined by directional derivatives, and prove it is…

A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…

Let $\Pi$ be a polar space of rank $n$ and let ${\mathcal G}_{k}(\Pi)$, $k\in \{0,\dots,n-1\}$ be the polar Grassmannian formed by $k$-dimensional singular subspaces of $\Pi$. The corresponding Grassmann graph will be denoted by…

The amplituhedron is a semialgebraic set given as the image of the non-negative Grassmannian under a linear map subject to a choice of additional parameters. We define the limit amplituhedron as the limit of amplituhedra by sending one of…

Given a vector space $V$ of homogeneous polynomials of the same degree over an infinite field, consider a generic subspace $W$ of $V$. The main result of this paper is a lower-bound (in general sharp) for the dimensions of the spaces…

We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…

The definition of principal nest is supplemented with a system of frames that make possible the classification of combinatorial types for every level of the nest. As a consequence, we give necessary and sufficient conditions for the…

In this paper, we propose a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. Our approach involves introducing the concept of a…

The Grassmann angle improves upon similar angles between subspaces that measure volume contraction in orthogonal projections. It works in real or complex spaces, with important differences, and is asymmetric, what makes it more efficient…

In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree of these polynomials, here called projective, are simply…

We present a criterion of local Normal Embedding of a semialgebraic (or definable in an o-minimal structure) contained in $R^n$ in terms orders of contact of arcs. Namely, we prove that a semialgebraic set is normally embedded at a point x…

A theorem of the first author states that the cotangent bundle of the type $A$ Grassmannian variety can be embedded as an open subset of a smooth Schubert variety in a two-step affine partial flag variety. We extend this result to cotangent…

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

We find a class of algebras A satisfying the following property: for every nontrivial noncommutative polynomial, the linear span of all its values in A equals A. This class includes the algebras of all bounded and all compact operators on…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

If, for a subset S of Z^k, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-valued polynomials and, (c) by finitely many k-tuples of…