A subcube partition is a of the Boolean cube $\{0,1\}^n$ into subcubes. irreducible if only sub-partitions whose union are singletons and entire partition. tight it “mentions” all coordinates.
 We study extremal properties partitions: minimal size, weight, maximal number points, minimum dimension. also consider existence homogeneous partitions, in which subcubes have same dimensions. addit...

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible de...

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

We regard the shearlet group as a semidirect product group and show that its standard representation is,typically, a quasiregu- lar representation. As a result we can characterize irreducible as well as square-integrable subrepresentations of the shearlet group.

A bounded linear operator T on a complex Hilbert space H is irreducible if it has no reducing subspace other than the trivial ones (0) and H; it is strongly irreducible if every operator similar to T is irreducible. Equivalently, T is irreducible (resp. strongly irreducible) if the only projections (resp. idempotent operators) commuting with T are 0 and I. Since (strongly) irreducible operators...