Related papers: Ideals of Adjacent Minors

We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring. We give a lower bound on the Ananyan-Hochster…

We consider a combinatorial property isolated in the field of ideal convergence, a P-property for two ideals on natural numbers. We show that among selected ideals induced by disjoint families, not all pairs satisfy P-property for two…

We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated…

We describe a generating set for the initial ideal of simplicial toric ideals with respect to the graded reverse lexicographic order, using representations of elements of affine monoids as sums of irreducible elements. Although the…

In finite group theory, studying the prime graph of a group has been an important topic for almost the past half-century. Recently, prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the…

The principal minors of a symmetric $n{\times}n$-matrix form a vector of length $2^n$. We characterize these vectors in terms of algebraic equations derived from the $ 2{\times}2{\times}2$-hyperdeterminant.

Let $I$ be an arbitrary ideal generated by binomials. We show that certain equivalence classes of fibers are associated to any minimal binomial generating set of $I$. We provide a simple and efficient algorithm to compute the indispensable…

In this paper we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.

We study initial algebras of determinantal rings, defined by minors of generic matrices, with respect to their classical generic point. This approach leads to very short proofs for the structural properties of determinantal rings. Moreover,…

We provide a complete description of the ideal that serves as the resultant ideal for n univariate polynomials of degree d. We in particular describe a set of generators of this resultant ideal arising as maximal minors of a set of…

Polyomino ideals, defined as the ideals generated by the inner $2$-minors of a polyomino, are a class of binomial ideals whose algebraic properties are closely related to the combinatorial structure of the underlying polyomino. We provide a…

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. These mesoprimary…

In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gr\"obner basis, due to combinatorial properties of the polyomino itself. Moreover, we…

Given a square matrix $A$ with entries in a commutative ring $S$, the ideal of $S[X]$ consisting of polynomials $f$ with $f(A) =0$ is called the null ideal of $A$. Very little is known about null ideals of matrices over general commutative…

Let $\KX =K\langle X_1,\ldots ,X_n\rangle$ be the free algebra generated by $X=\{ X_1,\ldots ,X_n\}$ over a field $K$. It is shown that with respect to any weighted $\mathbb{N}$-gradation attached to $\KX$, minimal homogeneous generating…

The notion off-ideals is recent and has been studied in the papers[1] [2], [5], [10], [11], [12], [13], [14] and [15]. In this paper, we have generalized the idea off-ideals to quasi f-ideals. This extended class of ideals is much bigger…

We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also…

We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generated by powers of linear generic forms of the corresponding…

We show that the ideal generated by maximal minors (i.e., $(k+1)$-minors) of a $(k+1) \times n$ Vandermonde matrix is radical and Cohen-Macaulay. Note that this ideal is generated by all Specht polynomials with shape $(n-k,1,...,1)$.

We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.