A linear ordering is scattered if it does not contain a copy of the rationals. Hausdorff characterised the class of scattered linear orderings as the least family of linear orderings that includes the class B of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in B. More generally, say that a partial ordering is κ-scattered if it does not contain...

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators de ned on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a par...

* Correspondence: [email protected] College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China Abstract Some results relating to the block matrix partial orderings and the submatrix partial orderings are given. Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product. Several equivalent conditions for the min...

The Partial Orders Framework 3] provides a uniied way to specify the memory semantics of distributed systems. This report demonstrates the usefulness of this framework for reasoning about the behavior of the shared memory of existing multiprocessors. Three bus-based machine models are examined: total ordering, total store ordering, and partial store ordering. A formal and unambiguous descriptio...

Adding symmetry breaking constraints is one of the oldest ways of breaking variable symmetries for CSPs. For instance, it is well known that all the symmetries for the pigeon hole problem can be removed by ordering the variables. We have generalized this result to all CSPs where the variables are subject to an all different constraint. In such case it is possible to remove all variable symmetri...