A Recursive Construction of Resolvable 2-(p^r, p, 1) Designs with Free Row Permutations, and Anti-Pasch Kirkman Triple Systems of Order 3^r
Abstract
This method generalizes the familiar vertical, horizontal, and diagonal lines of \(AG(2,p)\) and provides a direct computational tool for constructing affine and projective block designs, including the resolvable designs used in Kirkman systems. Because the algorithm uses only modular integer arithmetic, it offers a transparent and implementation‑friendly way to generate all blocks of the resolvable \(2\)-\((p^n,p,1)\) design arising from affine geometry.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Finite Group Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 1 March 2026
- Language
- EN
- Document type
- Preprint