Provan and Billera defined the notion of weak k-decomposability for pure simplicial complexes in the hopes of bounding the diameter of convex polytopes. They showed the diameter of a weakly k-decomposable simplicial complex ã is bounded above by a polynomial function of the number of k-faces in ã and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of verti...

Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied...

Let G be a graph of order n and r , 1 ≤ r ≤ n, a fixed integer. G is said to be r -vertex decomposable if for each sequence (n1, . . . , nr ) of positive integers such that n1 + · · · + nr = n there exists a partition (V1, . . . , Vr ) of the vertex set of G such that for each i ∈ {1, . . . , r}, Vi induces a connected subgraph of G on ni vertices. G is called arbitrarily vertex decomposable if...

Even the most super cial glance at the vast majority of crossing-minimal geometric drawings of Kn reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply 3-symmetric). And second, they all are 3-decomposable, that is, there is a triangle T enclosing the drawing, and a balanced partition A,B, C of the underlying set of points P , such that the orthogo...

This paper studies the impact of task complexity and decomposability on the degree of organizational divisionalization and hierarchy within firms. Drawing upon the team theory and modularity literature, it argues that the degree of divisionalization is predicated not only on the extent of interdependence (complexity) among tasks but also on the extent to which those interdependent relationships...

Even the most superficial glance at the vast majority of crossing-minimal geometric drawings of Kn reveals two hard-to-miss features. First, all such drawings appear to be 3-fold symmetric (or simply 3-symmetric) . And second, they all are 3-decomposable, that is, there is a triangle T enclosing the drawing, and a balanced partition A,B,C of the underlying set of points P , such that the orthog...

We study Hoeffding decomposable exchangeable sequences with values in a finite set D = {d1, . . . , dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

This paper is devoted to the study of higher secant varieties of varieties of completely decomposable forms. The main goal is to develop methods to inductively verify the non-defectivity of such secant varieties. As an application of these methods, we will establish the existence of large families of non-defective secant varieties of “small” varieties of completely decomposable forms.

Balister [Combin. Probab. Comput. 12 (2003), 1–15] gave a necessary and sufficient condition for a complete multigraph Kn to be arbitrarily decomposable into closed trails of prescribed lengths. In this article we solve the corresponding problem showing that the multigraphs Kn are arbitrarily decomposable into open trails.

We give a classification of the triples (g, g′, q) such that Zuckerman’s derived functor (g,K)-module Aq(λ) for a θ-stable parabolic subalgebra q is discretely decomposable with respect to a reductive symmetric pair (g, g′). The proof is based on the criterion for discretely decomposable restrictions by the first author and on Berger’s classification of reductive symmetric pairs.