4,110 research outputs found
Graded and Filtered Fiber Functors on Tannakian Categories
We study fiber functors on Tannakian categories which are equipped with a
grading or a filtration. Our goal is to give a comprehensive set of
foundational results about such functors. A main result is that each filtration
on a fiber functor can be split by a grading fpqc-locally on the base scheme
On the least exponential growth admitting uncountably many closed permutation classes
We show that the least exponential growth of counting functions which admits
uncountably many closed permutation classes lies between 2^n and
(2.33529...)^n.Comment: 13 page
Electronic properties of correlated metals in the vicinity of a charge order transition: optical spectroscopy of -(BEDT-TTF)Hg(SCN) ( = NH, Rb, Tl)
The infrared spectra of the quasi-two-dimensional organic conductors
-(BEDT-TTF)Hg(SCN) ( = NH, Rb, Tl) were measured in
the range from 50 to 7000 \cm down to low temperatures in order to explore the
influence of electronic correlations in quarter-filled metals. The
interpretation of electronic spectra was confirmed by measurements of pressure
dependant reflectance of -(BEDT-TTF)KHg(SCN) at T=300 K. The
signatures of charge order fluctuations become more pronounced when going from
the NH salt to Rb and further to Tl compounds. On reducing the temperature,
the metallic character of the optical response in the NH and Rb salts
increases, and the effective mass diminishes. For the Tl compound, clear
signatures of charge order are found albeit the metallic properties still
dominate. From the temperature dependence of the electronic scattering rate the
crossover temperature is estimated below which the coherent charge-carriers
response sets in. The observations are in excellent agreement with recent
theoretical predictions for a quarter-filled metallic system close to charge
order
The Queue-Number of Posets of Bounded Width or Height
Heath and Pemmaraju conjectured that the queue-number of a poset is bounded
by its width and if the poset is planar then also by its height. We show that
there are planar posets whose queue-number is larger than their height,
refuting the second conjecture. On the other hand, we show that any poset of
width has queue-number at most , thus confirming the first conjecture in
the first non-trivial case. Moreover, we improve the previously best known
bounds and show that planar posets of width have queue-number at most
while any planar poset with and has queue-number at most its
width.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th
International Symposium on Graph Drawing and Network Visualization (GD 2018
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