Realizing partitions respecting full and partial order information

Realizing partitions respecting full and partial order information

For n ∈ , we consider the problem of partitioning the interval [0, n) into k subintervals of positive integer lengths `1, . . . , `k such that the lengths satisfy a set of simple constraints of the form `i ij `j where ij is one of <, >, or =. In the full information case, ij is given for all 1 ≤ i, j ≤ k. In the sequential information information case, ij is given for all 1 < i < k and j = i ± ...

A partial order on partitions and the generalized Vandermonde determinant

We introduce a partial order on partitions which permits an inductive proof on partitions. As an example of this technique, we reprove the discriminant formula for the generalized Vandermonde determinant.  2003 Elsevier Inc. All rights reserved.

Realizing nurses’ full potential

Bisimulation Respecting First Order Operations

We identify two features of common process algebra operations their rst order avour and the fact that they respect bisimulation in a uniform manner For this purpose two notions are introduced rst a notion of rst order de nable operations on process graphs and second respect for sequence extension In the rst part of the paper those rst order de nable operations are characterised whose de ning fo...

Discretized Configurations and Partial Partitions

We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent to a wedge of spheres of dimension n− k+1. This space is homeomorphic to the order complex of the poset of ordered partial partitions of {1, . . . , n+1} with exactly k parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial...