Pigeonhole(Drawer) Principle

http://en.wikipedia.org/wiki/Pigeonhole_principle
In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

In a more quantified generalization: fornatural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that one of the sets will contain at least k + 1 objects.^[2] For arbitrary n and m this generalizes to k + 1 = ⌊(n - 1)/m⌋ + 1, where ⌊...⌋ is the floor function.

Though the most straightforward application is to finite sets (such as pigeons and boxes), it is also used with infinite sets that cannot be put into one-to-one correspondence. To do so requires the formal statement of the pigeonhole principle, which is "there does not exist an injective function on finite sets whosecodomain is smaller than its domain". Advanced mathematical proofs like Siegel's lemma build upon this more general concept.

下面再给出Ramsey定理的简单形式：
设p,q是正整数，p,q>= 2,则存在最小的正整数R(p,q),使得当n>=R(p,q)时，用红蓝两色涂色Kn的边，则或者存在一个蓝色的完全p边形，或者存在一个红色的完全q边形 。