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Heffter spaces.

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Title: Heffter spaces.
Authors: Buratti, M.1 (AUTHOR) marco.buratti@uniroma1.it, Pasotti, A.1,2 (AUTHOR) anita.pasotti@unibs.it
Source: Finite Fields & Their Applications. Sep2024, Vol. 98, pN.PAG-N.PAG. 1p.
Subjects: Orthogonal systems, Vector spaces, Finite fields
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 = 2 k w + 1 is a prime power with kw odd and k ≥ 3 , then there are at least ⌈ w 4 k 4 ⌉ mutually orthogonal k -cycle systems of order q. [ABSTRACT FROM AUTHOR]
Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 178638880
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PubType: Academic Journal
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  Data: 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 = 2 k w + 1 is a prime power with kw odd and k ≥ 3 , then there are at least ⌈ w 4 k 4 ⌉ mutually orthogonal k -cycle systems of order q. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Finite Fields & Their Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.ffa.2024.102464
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      – Code: eng
        Text: English
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      – SubjectFull: Orthogonal systems
        Type: general
      – SubjectFull: Vector spaces
        Type: general
      – SubjectFull: Finite fields
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      – TitleFull: Heffter spaces.
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            NameFull: Buratti, M.
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              M: 09
              Text: Sep2024
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              Y: 2024
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              Value: 98
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