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Gröbner bases for complete uniform families. (English) Zbl 1045.13011

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.

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
12Y05 Computational aspects of field theory and polynomials (MSC2010)
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References:

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