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Universal p ‐ary designs
Author(s) -
Jolliffe Liam
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21785
Subject(s) - mathematics
We investigate p ‐ary t ‐designs which are simultaneously designs for all t , which we call universal p ‐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.