Heffter spaces

IF 1.2 3区 数学 Q1 MATHEMATICS
M. Buratti , A. Pasotti
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引用次数: 0

Abstract

The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of r mutually orthogonal Heffter systems for any r. Such a set is equivalent to a resolvable partial linear space of degree r whose parallel classes are Heffter systems: this is a new combinatorial design that we call a Heffter space. We present a series of direct constructions of Heffter spaces with odd block size and arbitrarily large degree r obtained with the crucial use of finite fields. Among the applications we establish, in particular, that if q=2kw+1 is a prime power with kw odd and k3, then there are at least w4k4 mutually orthogonal k-cycle systems of order q.

赫夫特空间
赫夫特阵列的概念在过去十年中备受关注,它等价于一对正交赫夫特系统。在本文中,我们研究了任意 r 的 r 个相互正交的赫夫特系统集合的存在性问题。这样的集合等价于一个度数为 r 的可解析偏线性空间,其并行类是赫夫特系统:这是一种新的组合设计,我们称之为赫夫特空间。我们介绍了一系列直接构造的赫夫特空间,这些空间具有奇数块大小和任意大的度数 r,是利用有限域获得的。在这些应用中,我们特别指出,如果 q=2kw+1 是 kw 为奇数且 k≥3 的素数幂,那么至少有 ⌈w4k4⌉ 个相互正交的 q 阶 k 循环系统。
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来源期刊
CiteScore
2.00
自引率
20.00%
发文量
133
审稿时长
6-12 weeks
期刊介绍: Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
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