The discussion revolves around counting surjective functions from set A to set B, specifically when the cardinality of A is one greater than that of B. The participants explore the implications of this relationship in the context of combinatorial principles.
There are multiple interpretations of the counting problem being explored, with some participants suggesting specific formulas and others seeking proofs or further clarification on the reasoning behind these approaches. The conversation reflects a mix of attempts to derive a method and requests for validation of the proposed ideas.
Some participants note that the problem is not strictly homework but rather an inquiry into a mathematical concept. There is also a mention of the importance of self-discovery in the learning process, emphasizing the forum's guidelines.
StopWatch said:Homework Statement
Count all surjections of A to B, (f: A ---> B) where |A| = |B| + 1
Homework Equations
None? This is just a problem I came across online.
The Attempt at a Solution
I'm really not sure. This isn't technically homework, but I'm just looking for a good method. I thought maybe the pigeonhole principle might help?
Here's a somewhat easier problem that may help.StopWatch said:Homework Statement
Count all surjections of A to B, (f: A ---> B) where |A| = |B| + 1
Homework Equations
None? This is just a problem I came across online.
The Attempt at a Solution
I'm really not sure. This isn't technically homework, but I'm just looking for a good method. I thought maybe the pigeonhole principle might help?
StopWatch said:Also could you point me to somewhere that would prove why this is true?
An important principle of these Forums is to help those who post questions to discover the solutions for themselves. It's not to give the answers.sunjin09 said:My apologies, the answer should be (n+1)!*n/2, because you first choose 2 element to map to a single slot, that is (n+1)n/2, then you permute the n groups of elements onto n slot, that's n!, so the total is (n+1)!*n/2