6
votes
Accepted
The category of Multisets and Spans: morphism composition and tensor product
One possibility is as follows. I'll think of a multiset as a finite set $X$ equipped with a multiplicity function $m_X \colon X \to \{1,2,3,\dotsc\}$. We can then define a morphism from $X$ to $Y$ ...
- 56.9k
3
votes
What is the "correct" category of multisets
I suspect that the notion of "multiset" is actually ambiguous. For instance, different notions will be appropriate when talking about bosons vs. fermions vs. distinguishable (but ...
- 63.9k
2
votes
Accepted
Counting multisets satisfying a fixed property
In other words, every element $x\in M\cap (S\setminus R)$ has even multiplicity $\nu(x)$, while the multiplicity of elements of $M\cap R$ is unrestricted.
Then, the generating functions is
\begin{...
- 34.3k
2
votes
The combinations of a finite multiset
It can be easily seen that $C(k;m_1,\dots,m_n)$ equals the coefficient of $x^k$ in
$$\prod_{i=1}^n (1+x+\dots+x^{m_i}) = \prod_{i=1}^n \frac{1-x^{m_i+1}}{1-x} = (1-x)^{-n} \prod_{i=1}^n (1-x^{m_i+1}).$...
- 34.3k
Only top scored, non community-wiki answers of a minimum length are eligible