0. Introduction. In this paper we consider factorizations of finite rank operators through finite-dimensional C∗-algebras. We are interested in factorization norms involving either the completely bounded norm ‖ ‖cb or Haagerup’s decomposable norm ‖ ‖dec (see [11]). Let us denote byMn the C∗-algebra of all n×n matrices with complex entries. Let A and B be two C∗-algebras, and let us consider a f...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. In this paper, we study the number of k-decomposable trees in families of increasing trees, i.e. labeled trees in which the unique path from the root to an arbitrary vertex forms an increasing sequence. Functional equations for the corresponding counting series are provided, yielding asymptotic or ev...

The union of two disjoint (n, 4n−1, 2) MDS codes in {0, 1, 2, 3}n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation in terms of n-quasigroups of order 4...

A systematic method for generating unlabelled combinatorial structures uniformly at random is presented. It applies to structures that are decomposable, i.e., formally speciiable by grammars involving unions, products, sequences, multisets and cycles. All such structures of size n can be generated uniformly by either sequential algorithms of worst-case arithmetic complexity O(n 2) or by \boustr...

Many constraint satisfaction problems can be naturally and efficiently modelled using non-binary constraints like the “all-different” and “global cardinality” constraints. Certain classes of these non-binary constraints are “network decomposable” as they can be represented by binary constraints on the same set of variables. We compare theoretically the levels of consistency which are achieved o...

According to Gestalt theory, any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The consists of numerous autogenerated substructures an inherent hierarchy far more smalls than larges. Through these substructures, the structural beauty (L), or equivalently livingness space, can be computed by multiplication number (S) thei...