Intersection theorems and mod p rank of inclusion matrices
Journal of Combinatorial Theory Series A
A diagonal form for the incidence matrices of t-subsets vs. k-subsets
European Journal of Combinatorics
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Remarks on recent formulas of Wilson and Frankl
European Journal of Combinatorics
On the density of sets of divisors
Discrete Mathematics
Sperner families of bounded VC-dimension
Discrete Mathematics
Hilbert function and complexity lower bounds for symmetric Boolean functions
Information and Computation
Concrete Math
Algebraic properties of modulo q complete ℓ-wide families
Combinatorics, Probability and Computing
The lex game and some applications
Journal of Symbolic Computation
Some combinatorial applications of Gröbner bases
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
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We describe (reduced) Gröbner bases of the ideal of polynomials over a field, which vanish on the set of characterisic vectors of the complete unifom families ({\scriptstyle [n]}\\[-4pt]{\scriptstyle d}). An interesting feature of the results is that they are largely independent of the monomial order selected. The bases depend only on the ordering of the variables. We can thus use past results related to the lex order in the presence of degree-compatible orders, such as deglex. As applications, we give simple proofs of some known results on incidence matrices.