English

Universal $p$-ary designs

Combinatorics 2020-12-09 v1

Abstract

We investigate pp-ary tt-designs which are simultaneously designs for all tt, which we call universal pp-ary designs. Null universal designs are well understood due to Gordon James via the representation theory of the symmetric group. We study non-null designs and determine necessary and sufficient conditions on the coefficients for such a design to exist. This allows us to classify all universal designs, up to similarity.

Cite

@article{arxiv.2012.04202,
  title  = {Universal $p$-ary designs},
  author = {Liam Jolliffe},
  journal= {arXiv preprint arXiv:2012.04202},
  year   = {2020}
}

Comments

10 pages, Comments welcome. arXiv admin note: substantial text overlap with arXiv:2010.09796

R2 v1 2026-06-23T20:48:17.596Z