Related papers: Rank weights for arbitrary finite field extensions
Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's.…
Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three.
In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which…
We study restriction problem in vector spaces over finite fields. We obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem, and we show that the range of the exponentials is sharp.
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
We consider a natural generalization of both locally finite irreducible root systems and extended affine root systems defined by Saito. We classify the systems.
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.
We find universal spaces for Alexandroff and finite spaces and explore some of its topological properties as well as their description as inverse limits of finite spaces and Alexandroff extensions. They can be used as a natural environment…
We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.
We prove a general version of the "Stability Theorem": if $K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $F|K$ is a finitely generated (transcendental) extension of…
In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Hamming metric. In this paper, we propose a new definition of…
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…
We prove that the partition rank and the analytic rank of tensors are equal up to a constant, over finite fields of any characteristic and any large enough cardinality depending on the analytic rank. Moreover, we show that a plausible…
We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is…
Some aspects of a mathematical theory of rigidity and flexibility are developed for general infinite frameworks and two main results are obtained. In the first sufficient conditions, of a uniform local nature, are obtained for the existence…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
In 2006, Gao and Zeng \cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we…