2,768 research outputs found
Path representation of maximal parabolic Kazhdan-Lusztig polynomials
We provide simple rules for the computation of Kazhdan--Lusztig polynomials
in the maximal parabolic case. They are obtained by filling regions delimited
by paths with "Dyck strips" obeying certain rules. We compare our results with
those of Lascoux and Sch\"utzenberger.Comment: v3: fixed proof of lemma
The model of dynamo with small number of modes and magnetic activity of T Tauri stars
The model that describes operation of dynamo in fully convective stars is
presented. It is based on representation of stellar magnetic field as a
superposition of finite number of poloidal and toroidal free damping modes. In
the frame of adopted low of stellar differential rotation we estimated minimal
value of dynamo number D, starting from which generation of cyclic magnetic
field in stars without radiative core is possible. We also derived expression
for period of the cycle. It was found that dynamo cycles of fully convective
stars and stars with thin convective envelopes differ in a qualitative way: 1)
distribution of spots over latitude during the cycle is different in these
stars; 2) the model predicts that spot formation in fully convective stars
should be strongly suppressed at some phases of the cycle.
We have analyzed historical lightcurve of WTTS star V410 Tau and found that
long term activity of the star is not periodic process. Rather one can speak
about quasi cyclic activity with characteristic time of yr and chaotic
component over imposed. We concluded also that redistribution of cool spots
over longitude is the reason of long term variations of V410 Tau brightness. It
means that one can not compare directly results of photometric observations
with predictions of our axially symmetric (for simplicity) model which allows
to investigate time evolution of spot's distribution over latitude. We then
discuss what kind of observations and in which way could be used to check
predictions of the dynamo theory.Comment: 18 pages, 5 figures, accepted to Astron. Let
Towards a combinatorial classification of skew Schur functions
We present a single operation for constructing skew diagrams whose
corresponding skew Schur functions are equal. This combinatorial operation
naturally generalises and unifies all results of this type to date. Moreover,
our operation suggests a closely related condition that we conjecture is
necessary and sufficient for skew diagrams to yield equal skew Schur functions.Comment: 34 pages, 2 figures. Minor changes. Final version, to appear in
Transactions of the AM
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