Universal $p$-ary designs
Combinatorics
2020-12-09 v1
Abstract
We investigate -ary -designs which are simultaneously designs for all , which we call universal -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