On the bases for trades Original Research Article

In recent years, the algebraic and combinatorial properties of inclusion matrices of t-subsets versus k-subsets of a v-set X have been the focus of attention by some authors. We first make a comparative study of the known bases for the Z-modules generated by trades (the elements of the null space of these matrices), and then, by utilizing these bases, we note that a large family of new bases can be produced.