- Published 1980 in SIAM J. Matrix Analysis Applications

It is possible to view the combinatorial structures known as (integral) t-designs as Z-modules in a natural way. In this note we introduce a polynomial associated to each such Z-module. Using this association, we quickly derive explicit bases for the important class of submodules which correspond to the so-called null-designs. Introduction. Among the most fundamental (and least understood) types of combinatorial configurations are the t-designs [2], [5], [6]. These can be defined as follows. Let v, k, and A be positive integers satisfying -< k <v. A t-design Sx (t, k, v) is a collection #9 of k-subsets B (called blocks) of a v-set V with the property that every t-subset of V occurs as a subset of exactly A blocks B . (It is not required that blocks be distinct.) It follows from this definition that for any <-t, the number of blocks of a t-design which contain a fixed/-subset I of V is exactly

@article{Graham1980OnTS,
title={On the Structure of t-Designs},
author={Ronald L. Graham and Shuo-Yen Robert Li and Wen-Ching Winnie Li},
journal={SIAM J. Matrix Analysis Applications},
year={1980},
volume={1},
pages={8-14}
}