Related papers: Binomial Difference Ideals
We call an ideal in a polynomial ring robust if it can be minimally generated by a universal Gr\"obner basis. In this paper we show that robust toric ideals generated by quadrics are essentially determinantal. We then discuss two possible…
A natural candidate for a generating set of the (necessarily prime) defining ideal of an $n$-dimensional monomial curve, when the ideal is an almost complete intersection, is a full set of $n$ critical binomials. In a somewhat modified and…
Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for…
In this paper, we investigate the arithmetical rank of a binomial ideal $J$. We provide lower bounds for the binomial arithmetical rank and the $J$-complete arithmetical rank of $J$. Special attention is paid to the case where $J$ is the…
We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing…
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…
We study the symbolic $F$-splitness of families of binomial edge ideals. We also study the strong $F$-regularity of the symbolic blowup algebras of families of binomial edge ideals. We make use of Fedder-like criteria and combinatorial…
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals.
In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.
The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese $3$-fold projections. More precisely, for any integer $d\ge 4$ and any $d$-th root $e$ of…
We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph…
Given a finite set of closed rational points of affine space over a field, we give a Gr\"obner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the…
In this note, we define and investigate ideal covering numbers of associative rings (not assumed to be commutative or unital): three invariants defined as the minimal number of proper left, right, or two-sided ideals whose union equals the…
In this article, we investigate the combinatorial and algebraic properties of the lcm-lattice associated with the edge ideal of a hypergraph. Let $\H$ be a hypergraph, $I(\H)$ its corresponding edge ideal in a polynomial ring in $n$…
In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed…
The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (e.g., $\{0\})$ that are closed under the natural metric, but has no prime ideals closed under that metric; hence closed…
An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the…
Let $L$ be a distributive lattice and $R(L)$ the associated Hibi ring. We compute $\reg R(L)$ when $L$ is a planar lattice and give a lower bound for $\reg R(L)$ when $L$ is non-planar, in terms of the combinatorial data of $L.$ As a…