2,316 research outputs found
Belyi-extending maps and the Galois action on dessins d'enfants
We study the absolute Galois group by looking for invariants and orbits of
its faithful action on Grothendieck's dessins d'enfants. We define a class of
functions called Belyi-extending maps, which we use to construct new Galois
invariants of dessins from previously known invariants. Belyi-extending maps
are the source of the ``new-type'' relations on the injection of the absolute
Galois group into the Grothendieck-Teichmuller group. We make explicit how to
get from a general Belyi-extending map to formula for its associated invariant
which can be implemented in a computer algebra package. We give an example of a
new invariant differing on two dessins which have the same values for the other
readily computable invariants.Comment: 13 pages, 7 figures; submitted for publication; revisions are that
the paper now deals only with Galois invariants of dessins, and that material
is slightly expande
Intergenerational equity and stationarity
We consider quasi-orderings of infinite utility streams satisfying the strong Pareto axiom (i.e., Paretian quasi-orderings) and study the question of how strong a notion of intergenerational equity one can impose on these quasi-orderings without generating an impossibility theorem. Building on a result by Mitra and Basu (2007), we first show that there exist many possible extensions of the finite anonymity axiom that are satisfied by some Paretian quasiordering. Then we study how the additional requirement of stationarity `a la Koopmans (1960) affects this result. After proving a possibility theorem for this case, we demonstrate that stationarityimposes strong restrictions on the extendability of the finite anonymity axiom.
Wada Dessins associated with Finite Projective Spaces and Frobenius Compatibility
\textit{Dessins d'enfants} (hypermaps) are useful to describe algebraic
properties of the Riemann surfaces they are embedded in. In general, it is not
easy to describe algebraic properties of the surface of the embedding starting
from the combinatorial properties of an embedded dessin. However, this task
becomes easier if the dessin has a large automorphism group.
In this paper we consider a special type of dessins, so-called \textit{Wada
dessins}. Their underlying graph illustrates the incidence structure of finite
projective spaces \PR{m}{n}. Usually, the automorphism group of these dessins
is a cyclic \textit{Singer group} permuting transitively the
vertices. However, in some cases, a second group of automorphisms
exists. It is a cyclic group generated by the \textit{Frobenius automorphism}.
We show under what conditions is a group of automorphisms acting
freely on the edges of the considered dessins.Comment: 23 page
On the leximin and utilitarian overtaking criteria with extended anonymity
This paper studies the extensions of the infinte-horizon variants of the leximin principle and utilitarianism on the set of infinite utility streams. We especially examine those extensions which satisfy the axiom of Preference-continuity (or Consistency) and the extended anonymity axiom called Q-Anonymity. We formulate new extended leximin and utilitarian social welfare relations (SWRs), called Q-W-leximin SWR and Q-overtaking criterion respectively, and show that Weak Preference-continuity (or Weak Consistency) and Q-Anonymity together with Strong Pareto and Hammond Equity (resp. Partial Unit Comparability) characterize all SWRs that include the Q-W-leximin SWR (resp. the Q-overtaking criterion) as a subrelation. We also show that there exists no SWR satisfying Strong Pareto, Strong Preference-continuity (or Strong Consistency) and Q-Anonymity.Q-Anonymity, Preference-continuity, Consistency, Leximin, Utilitarianism, Overtaking criterion
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