A SIMPLE CONSTRUCTION OF KIRKMAN TRIPLE SYSTEMS OF ORDER 3h

Antonio Causa†, Leonardo Fragapane‡, Mario Gionfriddo§, Elena Guardo

Abstract: A Steiner triple system (STS) of order v is a 3-uniform hypergraph with v vertices in which every 2-subset of vertices has degree 1. A Kirkman triple system (KTS) is a resolvable Steiner triple system, that is, a partition of the blocks of the triple system into classes which are themselves partitions of the set of vertices into disjoint blocks. In this paper we give a construction of KTS of order v = 3h much simpler and less technical than previously known constructions.

Keywords: Kirkman triple systems, resolvable designs.

MSC: 05B07, 05B10.

DOI       10.56082/annalsarscimath.2026.2.225

Read full articleDYNAMICS OF THE ΛCDM MODEL OF THE UNIVERSE FROM THE PERSPECTIVE OF THE DYNAMICAL SYSTEMS THEORY                                                                                                                         Download articleDYNAMICS OF THE ΛCDM MODEL OF THE UNIVERSE FROM THE PERSPECTIVE OF THE DYNAMICAL SYSTEMS THEORY 

†causa@dmi.unict.it, Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria, 6- 95100- Catania, Italy
‡leonardo.fragapane@phd.unict.it, Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria, 6- 95100- Catania, Italy
§gionfriddo@dmi.unict.it, Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria, 6- 95100- Catania, Italy
guardo@dmi.unict.it, Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria, 6- 95100- Catania, Italy

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 2, 2026

       

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997