Skew Partitions

Specifications of SkewPartitions

This page is for discussing the specifications for the library combinat::skewPartitions

Hi there !

These are the new definitions for skewPartitions :

A skew partition skp is a list of two partitions [p, q], the second one (inner partition) included in the first one (outer partition). A skew partition is represented graphically by the boxes in the outer partition which are not in the inner partition. The overlap of two consecutive rows in a skew partition is the number of pairs of boxes (one in each row) which have a common edge. This number can be positive, zero or negative :

       ####           ####         ##
         ###              ##           ###
    overlap = 2    overlap = 0    overlap = -2
    connected      unconnected    disconnect

The overlap of a skp is the minimum of the overlaps of the consecutive rows, or infinity in the case of at most one row. If the overlap is positive, the skp is called "Connected" (reserved word).

Notes :

• any skewPartition of overlap N has also overlap N-1
• [[][]] has overlap infinity, size 0, rowLenghts [0] and is Connected
• {set of connected} included in {set of unconnected} included in {set of disconnected}
• disconnected is a word used only for description purposes (I have check my English dictionnary) Could someone confirm that it is ok to use "disconnected" in the doc ?

Regards

Teresa