The skew diagram poset and components of skew characters

Abstract

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.