40,995 research outputs found

    Lagrangianity for log extendable overconvergent FF-isocrystals

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    In the framework of Berthelot's theory of arithmetic D\mathcal{D}-modules, we prove that Berthelot's characteristic variety associated with a holonomic D\mathcal{D}-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 FF-isocrystal.Comment: arXiv admin note: substantial text overlap with arXiv:1411.293

    Degree Sequence Index Strategy

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    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 kk-independence and the kk-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 K1,rK_{1,r}-free graphs, we use DSI to generalize some results of Faudree, Gould, Jacobson, Lesniak and Lindquester
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