Work

$$\textrm{EA}(q)$$-additive Steiner 2-designs

Year: 2026

Type: article

Abstract: A design is G -additive, with G an abelian group, if its points are in G and each block is zero-sum in G . All the few known “manageable” additive Steiner 2-designs are $$\textrm{EA}(q)$$ EA ( q ) -additive for a suitable q , where $$\textrm{EA}(q)$$ EA ( q ) is the elementary abelian group of order q . We present some general constructions for $$\textrm{EA}(q)$$ EA ( q ) -additive Steiner 2-designs which unify the known ones and allow to find a few new ones: an $$\textrm{EA}(2^8)$$ EA ( 2 8 ) -additive 2-(52, 4, 1) design which is also resolvable, and three pairwise non-isomorphic $$\textrm{EA}(3^5)$$ EA ( 3 5 ) -additive 2-(121, 4, 1) designs, none of which is the point-line design of $$\textrm{PG}(4,3)$$ PG ( 4 , 3 ) . In the attempt to find also an $$\textrm{EA}(2^9)$$ EA ( 2 9 ) -additive 2-(511, 7, 1) design, we prove that a putative (subspace) 2-analog of a 2-(9, 3, 1) design cannot be cyclic.

Source: Journal of Algebraic Combinatorics

DOI: 10.1007/s10801-026-01535-6

Authors: Marco Buratti, Mario Galici, Alessandro Montinaro, Anamari Nakić, Alfred Wassermann

Institutions: Sapienza University of Rome, University of Salento, University of Zagreb, Faculty of Electrical Engineering and Computing in Zagreb, University of Bayreuth

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni