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...

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...