International Journal of Mathematics and Mathematical Sciences

Research Article

Discrete Dynamics by Different Concepts of Majorization

Table 3

The evaluation of the different concepts of perm-majorization. In the first column the time steps are given. One sees the relation × of the perm-majorization in the second column and the weak perm-submajorization in the third column. Incomparableness are denoted by 𝑘 = 𝑡 [ 𝑠 ] / 5 𝑠 .
ℎ ( 𝑘 ) 𝑅 ℎ ( 𝑘 + 1 ) ℎ ( 2 𝑘 ) 𝑅 ℎ ( 2 𝑘 + 2 ) 𝑓 ( 𝑘 ) 𝑅 𝑓 ( 𝑘 + 1 ) 𝑓 ( 2 𝑘 ) 𝑅 𝑓 ( 2 𝑘 + 2 ) p e r m ≻
0 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 p e r m ≻
1 p e r m ≻ 𝑤 p e r m ≻
2 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
3 p e r m ≻ 𝑤 ×
4 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
5 × ×
6 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
7 p e r m ≻ 𝑤 ×
8 p e r m ≻ × p e r m ≻ 𝑤 ×
9 p e r m ≻ 𝑤 ×
10 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
11 p e r m ≻ 𝑤 ×
12 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
13 p e r m ≻ 𝑤 ×
14 × × p e r m ≻ 𝑤 ×
15 p e r m ≻ 𝑤 ×
16 × × × ×
17 × ×
18 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
19 × ×
20 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
21 p e r m ≻ 𝑤 ×
22 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
23 × ×
24 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
25 p e r m ≻ 𝑤 ×
26 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
27 p e r m ≻ 𝑤 ×
28 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
29 × ×
30 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
31 p e r m ≻ 𝑤 ×
32 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
33 p e r m ≻ 𝑤 ×
34 × × p e r m ≻ 𝑤 ×
35 p e r m ≻ 𝑤 ×
36 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
37 p e r m ≻ 𝑤 ×
38 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
39 p e r m ≻ 𝑤 ×
40 p e r m ≻ p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
41 p e r m ≻ 𝑤 ×
42 × × p e r m ≻ 𝑤 ×
43 p e r m ≻ 𝑤 ×
44 × × p e r m ≻ 𝑤 ×
45 p e r m ≻ 𝑤 ×
46 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
47 p e r m ≻ 𝑤 ×
48 × p e r m ≻ 𝑤 p e r m ≻ 𝑤 ×
49 p e r m ≻ 𝑤 p e r m ≻
50 × 1 𝐼 ( ℎ ) = l o g 2 𝑛 𝑛 𝑖 = 1 𝑝 𝑖 , ( 4 . 2 )