Geodesic
Gröbner bases for complete uniform families
Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 171-180.

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Summary: 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 $( _{d} ^{[ n]} )$ (_text d^[n] ) . 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.
Keywords: Gröbner basis, uniform family, inclusion matrix, Hilbert function 
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     author = {Heged\'{u}s, G\'abor and R\'onyai, Lajos},
     title = {Gr\"obner bases for complete uniform families},
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     pages = {171--180},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2003__17_2_a1/}
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Hegedűs, Gábor; Rónyai, Lajos. Gröbner bases for complete uniform families. Journal of Algebraic Combinatorics, Tome 17 (2003) no. 2, pp. 171-180. http://geodesic.mathdoc.fr/item/JAC_2003__17_2_a1/