Partitionable sets, almost partitionable sets and their applications
Combinatorics
2023-11-27 v2
Abstract
This paper introduces almost partitionable sets to generalize the known concept of partitionable sets. These notions provide a unified frame to construct -cyclic patterned starter whist tournaments and cyclic balanced sampling plans excluding contiguous units. The existences of partitionable sets and almost partitionable sets are investigated. As an application, a large number of optical orthogonal codes achieving the Johnson bound or the Johnson bound minus one are constructed.
Cite
@article{arxiv.1911.07189,
title = {Partitionable sets, almost partitionable sets and their applications},
author = {Yanxun Chang and Simone Costa and Tao Feng and Xiaomiao Wang},
journal= {arXiv preprint arXiv:1911.07189},
year = {2023}
}