相关论文: Noncommutative Involutive Bases
Geometric involutive bases for polynomial systems of equations have their origin in the prolongation and projection methods of the geometers Cartan and Kuranishi for systems of PDE. They are useful for numerical ideal membership testing and…
We consider certain questions pertaining to noncommutative generalized Brownian motions with multiple processes. We establish a framework for generalized Brownian motion with multiple processes similar to that defined by Guta and prove…
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gr\"obner bases in not only algebras with straightening law (ASLs or Hodge…
A motivation to study Gr\"{o}bner theory for fields with valuations comes from tropical geometry, for example, they can be used to compute tropicalization of varieties \citep{maclagan2009introduction}. The computational aspect of this…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
The number of walks of $k$ steps from the node $\mathsf{0}$ to the node $\lambda$ on the representation graph (McKay quiver) determined by a finite group $\mathsf{G}$ and a $\mathsf{G}$-module $\mathsf{V}$ is the multiplicity of the…
Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that replaces each intermediate Groebner basis with its reduced…
This paper involves categories and computer science. The paper is motivated by a question which arises from two pieces of research. Firstly, the work of Brown and Heyworth which extends rewriting techniques to enable the computation of left…
Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A…
With this paper we present an extension of our recent ISSAC paper about computations of Groebner(-Shirshov) bases over free associative algebras Z<X>. We present all the needed proofs in details, add a part on the direct treatment of the…
It has been shown previously that a large class of monomial maps equivariant under the action of an infinite symmetric group have finitely generated kernels up to the symmetric action. We prove that these symmetric toric ideals also have…
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems…
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature…
In this article we produce Groebner bases for the defining ideal of a monomial curve that corresponds to an almost arithmetic sequence of positive integers, correcting previous work of Sengupta,(2003).
We generalize the Gr\"obner basis method for free D-modules to the case of several term orderings induced by a partition of the set of basic variables. Using this generalized Gr\"obner basis technique we prove the existence and give a…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
Signature-based algorithms are a popular kind of algorithms for computing Groebner basis, including the famous F5 algorithm, F5C, extended F5, G2V and the GVW algorithm. In this paper, an efficient method is proposed to solve the…
Blockwise determinantal ideals are those generated by the union of all the minors of specified sizes in certain blocks of a generic matrix, and they are the natural generalization of many existing determinantal ideals like the Schubert and…