4
votes
Accepted
Number of surjective mappings from set $A$ to set $B$
A function $f:A \to B$ assigns to each element of $A$ exactly one element of $B$.
In your case, each of the $6$ elements of $A$ has $4$ choices for its image in $B$.
Thus, the total number of ...
- 3,934
3
votes
Number of surjective mappings from set $A$ to set $B$
Towards "where did I go wrong":
There are two "types" of surjective functions from $A$ to $B$, corresponding to the two compositions
$6 = 3 + 1 + 1 + 1$
$6 = 2 + 2 + 1 + 1$
of 6 ...
- 24.5k
2
votes
Accepted
A non-transitive game league
Let $L$ be a league with the mean $m$, and let $M = \max\limits_{T_i} \max T_i$. Then $T = (3m - 2M - 2, M + 1, M + 1)$ wins against every team in $L$ on the second and third positions.
In case we ...
- 19.1k
2
votes
Number of surjective mappings from set $A$ to set $B$
Another way of counting these, is by observing that each surjective map is determined by the inverse image of each of the four elements in $B$.
Thus, the number of such maps is $4!$ times the number ...
- 14.2k
1
vote
Accepted
Necessary and sufficient condition for a subset of the powerset of $S$ to be the set of relation classes of some binary relation $R$ on $S$?
This happens iff $X$ is the surjective image of some quotient of $S$. By taking a further quotient, this is equivalent to $X$ being in bijection with some quotient of $S$.
If $i:S_\sim\cong X$ is a ...
- 269k
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