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Emptiness Problems for Integer Circuits
TLDR
It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity. Expand
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 andExpand
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. KonigExpand
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
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 theirExpand
Emptiness problems for integer circuits
TLDR
It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a well-studied, major open problem in algebraic computing complexity. Expand
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 monodromyExpand
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 knownExpand
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