The skew diagram poset and components of skew characters

We investigate the poset of skew diagrams ordered by adding or forming the union of skew diagrams. We will show that a skew diagram which has at least n convex corners to the upper left and also to the lower right is larger than the skew diagram consisting of n disconnected single boxes. Using this property, we obtain lower bounds for the number of components, constituents and pairs of components which differ by one box in a given skew character.