Block designs and systems of pairs

Alexander Shramchenko; Vasilisa Shramchenko

Block designs and systems of pairs

Combinatorics 2026-07-20 v1

Authors: Alexander Shramchenko , Vasilisa Shramchenko

Abstract

We propose a new way to construct one block design from another, thus linking some block designs in a new way. At the same time, we find relationships between block designs and systems of pairs. Some of these relationships are established, another one is conjectured.

Keywords

block designs systems of pairs combinatorial designs construction methods

Cite

@article{arxiv.2607.18499,
  title  = {Block designs and systems of pairs},
  author = {Alexander Shramchenko and Vasilisa Shramchenko},
  journal= {arXiv preprint arXiv:2607.18499},
  year   = {2026}
}

Comments

12 pages