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Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on Râ€¦ (More)

We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacyâ€¦ (More)

We present a new approach to the ideal membership problem for polynomial rings over the integers: given polynomials f0, f1, . . . , fn âˆˆ Z[X], where X = (X1, . . . , XN ) is an N -tuple ofâ€¦ (More)

- Matthias Aschenbrenner, Christopher J. Hillar
- ISSAC
- 2008

A symmetric ideal I âŠ‚ R = K[x1,x2,...] is an ideal that is invariant under the natural action of the infinite symmetric group. We give an explicit algorithm to find Grobner bases for symmetric idealsâ€¦ (More)

- Matthias Aschenbrenner
- J. Comb. Theory, Ser. A
- 2012

A proof of a conjecture by Shadrin and Zvonkine, relating the entries of a matrix arising in the study of Hurwitz numbers to a certain sequence of rational numbers, is given. The main tools used areâ€¦ (More)

Asymptotic couples (of H-type) try to capture the structure induced by the derivation of a Hardy field K on the value group of the natural valuation on K. In this note we continue the study ofâ€¦ (More)

We introduceH-fields as ordered differential fields of a certain kind. Hardy fields extendingR, as well as the field of logarithmicexponential series over R areH-fields. We study Liouville extensionsâ€¦ (More)

- Matthias Aschenbrenner, Alf Dolich, Deirdre Haskell, Dugald Macpherson, Sergei Starchenko
- Notre Dame Journal of Formal Logic
- 2013

We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weaklyâ€¦ (More)

We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals isâ€¦ (More)

- Matthias Aschenbrenner, Raymond Hemmecke
- Foundations of Computational Mathematics
- 2007

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many â€œbuildingâ€¦ (More)