Related papers: On the weak Lefschetz property for almost complete…

The second Veronese ideal $I_n$ contains a natural complete intersection $J_n$ generated by the principal $2$-minors of a symmetric $(n\times n)$-matrix. We determine subintersections of the primary decomposition of $J_n$ where one…

Let $I=I(D)$ be the edge ideal of a weighted oriented graph $D$, let $G$ be the underlying graph of $D$, and let $I^{(n)}$ be the $n$-th symbolic power of $I$ defined using the minimal primes of $I$. We prove that $I^2=I^{(2)}$ if and only…

In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following. Theorem: For any positive integer $D$ and any integers $i,j$ $(0\leq i,j \leq D)$, the absolute value of the following hypergeometric series is at…

We study the order theoretic properties of relative weak injectivity, w.r.i., in short, in the category of C*-algebras. We prove that Arveson's extension theorem, with additional order assumption on the morphisms, is tightly connected with…

Fr\"oberg's classical theorem about edge ideals with $2$-linear resolution can be regarded as a classification of graphs whose edge ideals have linearity defect zero. Extending his theorem, we classify all graphs whose edge ideals have…

This paper gives a necessary and sufficient condition for Gorensteinness in Rees algebras of the $d$-th power of parameter ideals in certain Noetherian local rings of dimension $d\ge 2$. The main result of this paper produces many…

Motivated by the study of greedy algorithms for graph coloring, Bernshteyn and Lee introduced a generalization of graph degeneracy, which is called weak degeneracy. In this paper, we show the lower bound of the weak degeneracy for…

Let $k$ be a field of characteristic $0$. Using the method of idealization, we show that there is a non-Koszul, quadratic, Artinian, Gorenstein, standard graded $k$-algebra of regularity $3$ and codimension $8$, answering a question of…

MacMahon enumerated the plane partitions in an $a \times b \times c$ box. These are in bijection to lozenge tilings of a hexagon, to certain perfect matchings, and to families of non-intersecting lattice paths. In this work we consider more…

We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which…

For a complex number $x$, $\Vert x\Vert:=\min\{|x-m|:m\in\mathbb{Z}\}$. Let $k\geq 1$ be an integer, and $K$ be a number field. Let $\alpha_1,\ldots,\alpha_k$ be algebraic numbers with $|\alpha_i|\geq 1$ and let $d_i$ denotes the degree of…

Let L be the Leavitt path algebra of an arbitrary directed graph E over a field K. This survey article describes how this highly non-commutative ring L shares a number of the characterizing properties of a Dedekind domain or a Pr\"ufer…

Let us denote the nth difference between consecutive primes by d_n. The Prime Number Theorem clearly implies that d_n is logn on average. Paul Erd\H{o}s conjectured about 60 years ago that the sequence d_n/logn is everywhere dense on the…

Gordan and Noether proved in their fundamental theorem that an hypersurface $X=V(F)\subseteq \mathbb{P}^n$ with $n\leq 3$ is a cone if and only if $F$ has vanishing hessian (i.e. the determinant of the Hessian matrix). They also showed that…

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in $[Wi]$)…

We prove that second and higher powers of the edge ideals of anticycles admit linear quotient orderings, although the edge ideals themselves do not, thus resolving an open question of Hoefel and Whieldon in the affirmative and providing the…

Let K be the face ring of the independence complex of a matroid. We show that if T is a generic linear system of parameters, then K/T satisfies a weak form of the Hard Lefschetz Theorem. As a result, the first half of the h-vector of the…

This paper is devoted to studies of IwQN-spaces and some of their cardinal characteristics. Recently, \v{S}upina proved that I is not a weak P-ideal if and only if any topological space is an IQN-space. Moreover, under…

We show that the Strong Lefschetz Property in degree 1 for a homogeneous 0-dimensional complete intersection holds if the corresponding associated form, the Macaulay inverse systems, has a non-zero discriminant.

One deals with r-regular bipartite graphs with 2n vertices. In a previous paper Butera, Pernici, and the author have introduced a quantity d(i), a function of the number of i-matchings, and conjectured that as n goes to infinity the…