Related papers: Symmetric Complete Intersections
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals in an algebra of differential operators.
Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gr\"obner basis of the defining ideal $J$ of $A$ we give a condition, called the x-condition, which implies that all graded…
In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed in the partition forms. In particular, more zeros of self conjugate partitions beside odd permutations are heavily investigated.
We consider ideals in a polynomial ring generated by collections of power sum polynomials, and obtain conditions under which these define complete intersection rings, normal domains, and unique factorization domains. We also settle a key…
We study the intersection of the totally positive part of a split semisimple group over the real numbers with a totally positive parabolic subgroup.
A spline is an assignment of polynomials to the vertices of a graph whose edges are labeled by ideals, where the difference of two polynomials labeling adjacent vertices must belong to the corresponding ideal. The set of splines forms a…
Let $R$ be a commutative ring with nonzero identity and $I$ a proper ideal of $R$. The {\it ideal-based zero-divisor graph} of $R$ with respect to the ideal $I$, denoted by $\Gamma_I(R)$, is the graph on vertices $\{x \in R\setminus I \mid…
We present a class of toric varieties $V$ which, over any algebraically closed field of characteristic zero, are defined by codim $V$+1 binomial equations.
A symmetric chain of ideals is a rule that assigns to each finite set $S$ an ideal $I_S$ in the polynomial ring $\mathbb{C}[x_i]_{i \in S}$ such that if $\phi \colon S \to T$ is an embedding of finite sets then the induced homomorphism…
In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.
We obtain the exact values for depth and projective dimension and lower bounds for Stanley depth of the quotient rings of the edge ideals associated with all cubic circulant graphs.
In this paper, we provide a combinatorial characterization of those collections of cells whose inner $2$-minor ideals are complete intersections. More precisely, given a collection of cells $\mathcal C$ and its associated inner $2$-minor…
Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and…
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…
Given that symbolic and ordinary powers of an ideal do not always coincide, we look for conditions on the ideal such that equality holds for every natural number. This paper focuses on studying the equality for Derksen ideals defined by…
We discuss conditions for complete intersections in a toric variety which allow to compute Hodge numbers if the complete intersection is a quasi-smooth complete variety. A preliminary step is the computation of the Euler characteristic of…
In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…