Triangle decompositions of PG(n-1,2)

Triangle decompositions of PG(n-1,2) Full article

Journal

Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X

Output data

Year: 2026, Volume: 349, Number: 1, Article number : 114664, Pages count : 13 DOI: 10.1016/j.disc.2025.114664

Tags

subspace design, graph decomposition, triangle design, Heffter's difference problem

Authors

Shi M. ¹ , Li X. ¹ , Krotov D.S. ²

Affiliations

1	Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, 230601, China
2	Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, Novosibirsk, Russia 630090

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0017

We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common point. A triangle design is balanced if all points are involved in the same number of triangles. We construct balanced triangle designs in PG$(n-1,2)$ for all admissible $n$ (congruent to $1$ modulo $6$) and an infinite class of balanced block-divisible triangle designs. We also prove that the existence of a triangle design in PG$(n-1,2)$ invariant under the action of the Singer cycle group is equivalent to the existence of a partition of $Z_{2^n-1}\backslash\{0\}$ into special $18$-subsets and find such partitions for $n=7$, $13$, $19$.

Shi M. , Li X. , Krotov D.S.
Triangle decompositions of PG(n-1,2)
Discrete Mathematics. 2026. V.349. N1. 114664 :1-13. DOI: 10.1016/j.disc.2025.114664 WOS Scopus OpenAlex

Submitted:	Jan 23, 2024
Accepted:	Jun 23, 2025
Published print:	Jul 7, 2025
Published online:	Jul 7, 2025

Web of science:	WOS:001529807400001
Scopus:	2-s2.0-105009863604
OpenAlex:	W4412067509

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