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Emptiness Problems for Integer Circuits

- D. Barth, Moritz Beck, T. Dose, Christian Glaßer, Larissa Michler, Marc Technau
- Mathematics, Computer Science
- MFCS
- 2017

TLDR

Explicit Polynomials Having the Higman-Sims Group as Galois Group over Q(t)

We compute explicit polynomials having the sporadic Higman-Sims group HS and its automorphism group Aut(HS) as Galois groups over the rational function field Q(t).

Explicit Belyi maps over Q having almost simple primitive monodromy groups

We present all Belyi maps P^1(C) -> P^1(C) having almost simple primitive monodromy groups (not isomorphic to A_n or S_n) containing rigid and rational generating triples of degree between 50 and… Expand

Belyi map for the sporadic group J1

We compute the genus 0 Belyi map for the sporadic Janko group J1 of degree 266 and describe the applied method. This yields explicit polynomials having J1 as a Galois group over K(t), [K:Q] = 7.

A family of 4-branch-point covers with monodromy group PSL(6,2)

We describe the explicit computation of a family of 4-branch-point rational functions of degree 63 with monodromy group PSL(6,2). This, in particular, negatively answers a question by J. Konig… Expand

The non-existence of sharply 2-transitive sets of permutations in $$\mathrm {Sp}(2d,2)$$Sp(2d,2) of degree $$2^{2d-1}\pm 2^{d-1}$$22d-1±2d-1

- D. Barth
- Mathematics
- 16 February 2016

We use Müller and Nagy’s method of contradicting subsets to give a new proof for the non-existence of sharply 2-transitive subsets of the symplectic groups $$\mathrm {Sp}(2d,2)$$Sp(2d,2) in their… Expand

Emptiness problems for integer circuits

- D. Barth, Moritz Beck, T. Dose, Christian Glaßer, Larissa Michler, Marc Technau
- Mathematics, Computer Science
- Theor. Comput. Sci.
- 6 July 2020

TLDR

On Elkies' method for bounding the transitivity degree of Galois groups

In 2013 Elkies described a method for bounding the transitivity degree of Galois groups. Our goal is to give additional applications of this technique, in particular verifying that the monodromy… Expand

A one-parameter family of degree 36 polynomials with PSp(6,2) as Galois group over Q(t)

We present a one-parameter family of degree 36 polynomials with the symplectic 2-transitive group PSp(6,2) as Galois group over Q(t).

Computation of Belyi maps with prescribed ramification and applications in Galois theory

Abstract We compute genus-0 Belyi maps with prescribed monodromy groups and verify the computed results. Among the computed examples are almost simple primitive groups that satisfy the well known… Expand

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