most recent 30 from http://mathoverflow.net 2013-06-20T01:34:22Z http://mathoverflow.net/feeds/user/14040 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/60130/number-of-non-injective-functions adam 2011-03-30T21:51:15Z 2011-03-30T21:51:15Z

<p>If A is finite domain, of size m, and B is a finite codomain, of size n.</p> <p>n,m >= 0 and m &lt; n</p> <p>How many functions (f: A -> B) are not injective?</p> <p>Since the size of the codomain is larger than the domain, the number of injective functions is (n choose m) * m!</p> <p>But how would one determine the number of non-injective functions?</p>