Gröbner bases for complete uniform families
The main result of the paper is the determination of a reduced Gröbner basis for the polynomial ideal over a field which vanishes on the set of characteristic vectors of the complete uniform families \({[n] \choose d}\) of \(d\)-subsets of \([n]=\{1,2, \ldots , n\}\). It turns out that the Gröbner basis is dependent only on the order of the variables. Applications to known combinatorial results are given.
scientific article; zbMATH DE number 1908576