|
Main article: Double counting (proof technique) Double counting is a technique that equates two expressions that count the size of a set in two ways. Pigeonhole principle Main article: Pigeonhole principle The pigeonhole principle states that if a items are each put into one of b boxes, where a > b, then one of the boxes contains more than one item. Using this one can, for example, demonstrate the existence of some element in a set with some specific properties. Method of distinguished element Main article: Method of distinguished element The method of distinguished element singles out a "distinguished element" of a set to prove some result. Generating function Main article: Generating function Generating functions can be thought of as polynomials with infinitely many terms whose coefficients correspond to terms of a sequence. This new representation of the sequence opens up new methods for finding identities and closed forms pertaining to certain sequences. The (ordinary) generating function of a sequence an is G(a_n;x)=\sum_{n=0}^{\infty}a_nx^n. Recurrence relation Main article: Recurrence relation A recurrence relation defines each term of a sequence in terms of the preceding terms. Recurrence relations may lead to previously unknown properties of a sequence, but generally closed-form expressions for the terms of a sequence are more desired. |
About us|Jobs|Help|Disclaimer|Advertising services|Contact us|Sign in|Website map|Search|
GMT+8, 2015-9-11 22:04 , Processed in 0.128109 second(s), 16 queries .
