
100 Polytope Projects
For Table 5.1 we make use of Fig. 5.2 and Fig. 5.7.
The level m = 0 corresponds to the vector 1, and the level m=1 to the
pair of vectors 10 and 11 that is to the numbers 2 and 11 in the composition
graph.
The associated matrix is:
M=
11
01
(5.6)
For the level m=2 the vectors are 100, 101, 110 and 111 corresponding
to 3, 21, 12 and 111 in the composition graph.
The associated matrix is:
M=
111
011
101
001
(5.7)
5.1.5 Pascal Graphs for Compositions
The composition of objects in a fi xed number of parts or boxes is of practical
interest too.
For example, there are four partitions of 3 objects in just 2 boxes and
these can be represented ...