
Compositions and DecompositionsCompositions and Decompositions 105
5.2.4 Entropy Calculus
A partition is identifi ed with a binary word “w” obtained by fi lling its ribbon
diagram from left to right and from top to bottom with “1” in the fi rst box
and in any box following a descent, “0” elsewhere.
It results a situation as that shown in Fig. 5.16.
Figure 5.16 shows the fi lling of cells for integer partition.
Figure 5.17 illustrates the partition-binary word correspondence
Fig. 5.16 Filling of integer partition.
Fig. 5.17 Partition-binary word correspondence.
1
1
1
1
1
1
1
1
1
1
1
1
1
0
01
1 00
1 0 0 0
0
ˆ
1 0
1
1 1
01
0
1
00
1
1
1
w=1111
1
1
1
0
w=1011
1 0 0
1
w=1001
1