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Results tagged with partitions
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user 287674
12
votes
3
answers
885
views
Set partitions and permanents
Let $a(n)=$ Number of ordered set partitions of $[n]$ such that the smallest element of each block is odd.
Example:
a(3) = 3: 123, 12|3, 3|12.
a(4) = 5: 1234, 124|3, 3|124, 12|34, 34|12. … For any positive integer $n$,
$$\operatorname{per}(B)=\frac{3-(-1)^n}{2}F(n)$$
where $F(n)$ is the Fubini numbers, i.e. the number of ordered partitions of $[n]$.
It is equivalent to
Conjecture 3. …
- 884
3
votes
Set partitions and permanents
Let $a_k(n)$ = Number of ordered set partitions of $[n]$ with precisely $k$ blocks such that the smallest element of each block is odd. …
- 884