28 citations · 336 across the 38 of their papers we have counts for
20 papers · 1 filter
Trinomial containment in polynomial ideals is undecidable
Tobias Boege, Anna Hofer, Thomas Kahle
We prove that deciding whether an ideal in a polynomial ring contains a trinomial is impossible on a Turing machine. More precisely, from an integer polynomial we compute gener…
No short polynomials vanish on bounded rank matrices
Jan Draisma, Thomas Kahle, Finn Wiersig
We show that the shortest nonzero polynomials vanishing on bounded-rank matrices and skew-symmetric matrices are the determinants and Pfaffians characterising the rank. Algebraical…
Short polynomials in determinantal ideals
Thomas Kahle, Finn Wiersig
We show that a determinantal ideal generated by -minors does not contain any nonzero polynomials with or fewer terms. Geometrically this means that any nonzero polynomial…
Hilbert-Poincaré series of parity binomial edge ideals and permanental ideals of complete graph
Do Trong Hoang, Thomas Kahle
We give an explicit formula for the Hilbert-Poincaré series of the parity binomial edge ideal of a complete graph or equivalently for the ideal generated by all …
Binomial edge ideals of cographs
Thomas Kahle, Jonas Krüsemann
We determine the Castelnuovo-Mumford regularity of binomial edge ideals of complement reducible graphs (cographs). For cographs with vertices the maximum regularity grows as $2…
Linear syzygies, hyperbolic Coxeter groups and regularity
Alexandru Constantinescu, Thomas Kahle, Matteo Varbaro
We show that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley--Reisner ring of its nerve. Using this connection between geometric…