93 research outputs found
Modular Groups, Visibility Diagram and Quantum Hall Effect
We consider the action of the modular group on the set of
positive rational fractions. From this, we derive a model for a classification
of fractional (as well as integer) Hall states which can be visualized on two
``visibility" diagrams, the first one being associated with even denominator
fractions whereas the second one is linked to odd denominator fractions. We use
this model to predict, among some interesting physical quantities, the relative
ratios of the width of the different transversal resistivity plateaus. A
numerical simulation of the tranversal resistivity plot based on this last
prediction fits well with the present experimental data.Comment: 17 pages, plain TeX, 4 eps figures included (macro epsf.tex), 1
figure available from reques
On the asymptotics of higher-dimensional partitions
We conjecture that the asymptotic behavior of the numbers of solid
(three-dimensional) partitions is identical to the asymptotics of the
three-dimensional MacMahon numbers. Evidence is provided by an exact
enumeration of solid partitions of all integers <=68 whose numbers are
reproduced with surprising accuracy using the asymptotic formula (with one free
parameter) and better accuracy on increasing the number of free parameters. We
also conjecture that similar behavior holds for higher-dimensional partitions
and provide some preliminary evidence for four and five-dimensional partitions.Comment: 30 pages, 8 tables, 4 figures (v2) New data (63-68) for solid
partitions added; (v3) published version, new subsection providing an
unbiased estimate of the leading for the leading coefficient added, some
tables delete
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