6,363 research outputs found
Effective Invariant Theory of Permutation Groups using Representation Theory
Using the theory of representations of the symmetric group, we propose an
algorithm to compute the invariant ring of a permutation group. Our approach
have the goal to reduce the amount of linear algebra computations and exploit a
thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at
http://www.springer.com
Twisted Permutation Codes
We introduce twisted permutation codes, which are frequency permutation
arrays analogous to repetition permutation codes, namely, codes obtained from
the repetition construction applied to a permutation code. In particular, we
show that a lower bound for the minimum distance of a twisted permutation code
is the minimum distance of a repetition permutation code. We give examples
where this bound is tight, but more importantly, we give examples of twisted
permutation codes with minimum distance strictly greater than this lower bound.Comment: 20 page
On computing Belyi maps
We survey methods to compute three-point branched covers of the projective
line, also known as Belyi maps. These methods include a direct approach,
involving the solution of a system of polynomial equations, as well as complex
analytic methods, modular forms methods, and p-adic methods. Along the way, we
pose several questions and provide numerous examples.Comment: 57 pages, 3 figures, extensive bibliography; English and French
abstract; revised according to referee's suggestion
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