In this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by Minimal Geometric Deformation approach. We use complexity factor as a complementary condition to close system differential equations. It is shown that for polynomial resulting solution can be matched with two different modified-vacuum geometries.

The cover polynomial introduced by Chung and Graham is a twovariate graph polynomial for directed graphs. It counts the (weighted) number of ways to cover a graph with disjoint directed cycles and paths, it is an interpolation between determinant and permanent, and it is believed to be a directed analogue of the Tutte polynomial. Jaeger, Vertigan, and Welsh showed that the Tutte polynomial is #...

In recent years a number of algorithms have been designed for the "inverse" computational problems of polynomial algebra—factoring polynomials, solving systems of polynomial equations, or systems of polynomial inequalities, and related problems—with running time considerably less than that of the algorithms which were previously known. (For the computational complexity of the "direct" problems ...

The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. ...