Zobrazeno 1 - 10
of 2 316
pro vyhledávání: '"13P10"'
In this article, we investigate the cardinality of Grobner basis under various orderings. We identify a family of polynomials F and a criteria for the monomial orderings such that the reduced Grobner basis is double exponential in cardinality. We als
Externí odkaz:
http://arxiv.org/abs/2411.17602
In this article, we study two fundamental questions on polyomino ideals which are radicality and primality. In order to study the question of radicality, we initiate the study of Knutson ideals among polyominoes. Knutson ideals were introduced by Con
Externí odkaz:
http://arxiv.org/abs/2411.16364
Autor:
Bordianu, Andreea I., Cimpoeas, Mircea
We study the Stanley depth and the Hilbert depth of the edge ideals of path graphs, cycle graphs, generalized star graphs and double broom graphs.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2411.10844
We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is set on pairs of plane algebraic curves which form a so-called Wronski s
Externí odkaz:
http://arxiv.org/abs/2411.10776
Autor:
Kling, Filip Jonsson, Lundqvist, Samuel, Mohammadi, Fatemeh, Orth, Matthias, Sáenz-de-Cabezón, Eduardo
For the almost complete intersection ideals $(x_1^2, \dots, x_n^2, (x_1 + \cdots + x_n)^k)$, we compute their reduced Gr\"obner basis for any term ordering, revealing a combinatorial structure linked to lattice paths, elementary symmetric polynomials
Externí odkaz:
http://arxiv.org/abs/2411.10209
Autor:
Higashitani, Akihiro
We introduce a new class of algebras arising from graphs, called binomial edge rings. Given a graph $G$ on $d$ vertices with $n$ edges, the binomial edge ring of $G$ is defined to be the subalgebra of the polynomial ring with $2d$ variables generated
Externí odkaz:
http://arxiv.org/abs/2411.07812
Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals. Thanks to the functorial properties of
Externí odkaz:
http://arxiv.org/abs/2410.17090
Autor:
Huang, Daoji, Larson, Matt
We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give simple proof
Externí odkaz:
http://arxiv.org/abs/2410.02135
Publikováno v:
Results Math. 79(2) (2024) Article 42
We obtain new invariant Einstein metrics on the compact Lie groups $\SO(n)$ which are not naturally reductive. This is achieved by using the real flag manifolds $\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)$ and by imposing certain symmetr
Externí odkaz:
http://arxiv.org/abs/2409.18990
Autor:
Kahle, Thomas, Vill, Julian
We propose an effective algorithm that decides if a prime ideal in a polynomial ring over the complex numbers can be transformed into a toric ideal by a linear automorphism of the ambient space. If this is the case, the algorithm computes such a tran
Externí odkaz:
http://arxiv.org/abs/2408.14323