HALL Theorem
Hall married Theorem (Hall's Marriage Theorem) ─ its application given this reason the British mathematician Philip
Hall asked. Let V and W as two separate groups, but the connection between V and W, a V, so that any
number of sets of element portions is S, and W which connect to a corresponding number of R (S). If | S | | R (S) |,
each element of the V and W can be found in a corresponding post of their own.
. Eg a bride Co. try to fix three boys: Jay (a), Andy (b), Su Youpeng (c) and 4 Female
Health: chiling (r), Patty (s), Chia-chi (t), Bianca Bai ( u). If you like Jay Chou and Lin Chi Hou
Pei Cen, like Andy and Patty Bai Xin Hui, Su Youpeng like Lin Chi-ling, Chia-chi and Bai Xin Hui, so
if the boys can be assigned to each beloved woman?
(Solution): If S
. 1
= {A, B, C}, then R & lt (Sl
) = {R & lt, S, T, U}, then
| S
. 1
| =. 3 <. 4 = | R & lt (Sl
) |
If S2
= {a, b}, then R & lt (S2
) = {R & lt, S, U}, then
| S2
| = 2 <. 3 = | R & lt (S2
) |
If S3
= {A, C}, then R & lt (S3
) = {r, s, t, u}, so
| S3
| = 2 <. 4 = | R & lt (S3
) |
If S4
= {B, C}, then R & lt (S4
) = {R & lt, S, T, U} , then
| S4
| 2 = <. 4 = | R & lt (S4
) |
∴ can be assigned to each male beloved woman!
. Eg a bride Co. try to fix three boys: Takeshi (a), Peng Cheng-min (b), Zhangjia Hao (c) and 4 female
students: Chris Ke (r), Xu Chunmei (s), Cai Shuzhen (t), flowery (u). If you like Takeshi Kaneshiro Chris Ke and Cai Shu
Zhen, Peng Cheng-min just like Cai Shuzhen, Zhang Jiahao like Chris Ke and Cai Shuzhen, then whether each boy Duke
to go with the beloved woman?
(Solution): If S = {a, b, c }, then R (S) = {r, t}, then
| S |. 3 => 2 = | R & lt (S) |
∴ not every boy can be equipped to the beloved woman!
For example Takeshi Kaneshiro married Chris Ke Peng Cheng-min and marry Cai Shuzhen, the Zhang
Hao will not marry a beloved woman. Similarly, if Zhang Jiahao married
Chris Ke Peng Cheng-min and marry Cai Shuzhen, the heart Takeshi Kaneshiro will not marry
a woman of love.
Author: Mars Shiyi Lang
Source: http://www.cnblogs.com/hxsyl/
