Permanental Ideals

permanental ideals 的 v 数

The v-numbers of permanental ideals

本文计算了通用、通用对称和通用Hankel矩阵的2×2 permanental ideals的v数。

2 x 2 permanental ideals of hypermatrices

We study the structure of ideals generated by some classes of 2 \times 2 permanents of hypermatrices. This generalizes [9] on 2 x 2 permanental ideal of generic matrices. We compare the obtained structure to that of the corresponding determinantal ideals in [Swanson-Taylor 11]: while the notion of t-switchability introduced in [11] plays a role for both permanental and determinantal ideals, the permanents require further restrictions, which in general increases the number of minimal primes. In the last two section we examine a few related classes of permanental ideals. This is an extension of …

Hilbert-Poincaré series of parity binomial edge ideals and permanental ideals of complete graph

We give an explicit formula for the Hilbert-Poincaré series of the parity binomial edge ideal of a complete graph $K_{n}$ or equivalently for the ideal generated by all $2\times 2$-permanents of a $2\times n$-matrix. It follows that the depth and Castelnuovo-Mumford regularity of these ideals are independent of $n$.

Permanental ideals of Hankel matrices

We provide the Grobner basis and the primary decomposition of the ideals generated by 2 by 2 permanents of Hankel matrices.

Minimal Primes Over Permanental Ideals

In this paper we discuss minimal primes over permanental ideals of generic matrices. We give a complete list of the minimal primes over ideals of 3 x 3 permanents of a generic matrix, and show that there are monomials in the ideal of maximal permanents of a d x 2d-1 matrix if the characteristic of the ground field is sufficiently large. We also discuss the Alon-Jaeger-Tarsi Conjecture, using our results and techniques to strenthen the previously known results.

对称矩阵的永久子式理想

Permanental ideals of symmetric matrices

本文研究对称矩阵的 $2\ imes 2$ 永久子式生成的理想 $P_2(X)$，计算其 Gröbner 基、维数、深度、极小素理想与准素分解，并揭示其代数性质依赖于基域特征是否为二。