17 citations · 53 across the 6 of their papers we have counts for
6 papers
Standard Bases in mixed Power Series and Polynomial Rings over Rings
Thomas Markwig, Yue Ren, Oliver Wienand
In this paper we study standard bases for submodules of a mixed power series and polynomial ring respectively of their localization with res…
New developments in the theory of Groebner bases and applications to formal verification
Michael Brickenstein, Alexander Dreyer, Gert-Martin Greuel +2
We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with…
The Groebner basis of the ideal of vanishing polynomials
G. -M. Greuel, F. Seelisch, O. Wienand
We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial w…
Convex Rank Tests and Semigraphoids
Jason Morton, Lior Pachter, Anne Shiu +2
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutation…
Three Counterexamples on Semigraphoids
Raymond Hemmecke, Jason Morton, Anne Shiu +2
Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection ar…
Geometry of rank tests
Jason Morton, Lior Pachter, Anne Shiu +2
We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equi…