The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is important to know for which thresholds one could utilize an ideal threshold sharing scheme and for which thresholds one would have to use nonideal schemes. The implication is that more than one...

Given a homogeneous ideal in polynomial ring over $\Bbb{C}$, we adapt the construction of Newton-Okounkov bodies to obtain convex subset Euclidean space such that suitable integral this set computes {\it Segre zeta function\/} ideal. That is, extract numerical information class subscheme projective from an associated (unbounded) set. The result generalizes arbitrary subschemes form previously k...

In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we will find an upper bound for the minimum distance and, i...

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

In this paper, we generalize the notions of a matrix and its ideal of 2 × 2 minors to that of a box-shaped matrix and its ideal of 2 × 2 minors, and make use of these notions to study projective embeddings of certain blowup surfaces. We prove that the ideal of 2× 2 minors of a generic box-shaped matrix is a perfect prime ideal that gives the algebraic description for the Segre embedding of the ...

Let S be a polynomial algebra over field. If I is the edge ideal of perfect semiregular tree, then we give precise formulas for values depth, Stanley projective dimension, regularity and Krull dimension S/I.

In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

In [2, Section 1.6] Peskine and Szpiro prove a theorem on adic approximations of finite free resolutions over local rings which, together with M. Artin's Approximation Theorem [1], allows them to "descend" modules of finite projective dimension over the completions of certain local rings to modules of finite projective dimension over finite etale extensions of those rings. In this note we will ...

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...