6533b7dcfe1ef96bd1271fbd

RESEARCH PRODUCT

An algebraic representation of Steiner triple systems of order 13

Marco Pavone

subject

Steiner triple systemZero (complex analysis)Steiner triple system STS Additive block designSTSCombinatoricsSet (abstract data type)Steiner systemIncidence structureHyperplaneSettore MAT/05 - Analisi MatematicaAlgebra representationQA1-939Order (group theory)Settore MAT/03 - GeometriaMathematicsVector spaceMathematicsAdditive block design

description

Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .

yearjournalcountryeditionlanguage
2021-11-01Examples and Counterexamples
10.1016/j.exco.2021.100013http://www.sciencedirect.com/science/article/pii/S2666657X21000082