40,995 research outputs found
Lagrangianity for log extendable overconvergent -isocrystals
In the framework of Berthelot's theory of arithmetic -modules,
we prove that Berthelot's characteristic variety associated with a holonomic
-modules endowed with a Frobenius structure has pure dimension. As
an application, we get the lagrangianity of the characteristic variety of a log
extendable overconvergent -isocrystal.Comment: arXiv admin note: substantial text overlap with arXiv:1411.293
Degree Sequence Index Strategy
We introduce a procedure, called the Degree Sequence Index Strategy (DSI), by
which to bound graph invariants by certain indices in the ordered degree
sequence. As an illustration of the DSI strategy, we show how it can be used to
give new upper and lower bounds on the -independence and the -domination
numbers. These include, among other things, a double generalization of the
annihilation number, a recently introduced upper bound on the independence
number. Next, we use the DSI strategy in conjunction with planarity, to
generalize some results of Caro and Roddity about independence number in planar
graphs. Lastly, for claw-free and -free graphs, we use DSI to
generalize some results of Faudree, Gould, Jacobson, Lesniak and Lindquester
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