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Results tagged with co.combinatorics
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user 47840
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Sum over integer compositions
Yes, there are closed-form expressions. The number $S(n,k)$ you are looking for is the number of weighted integer compositions with weighting function $f(a)=a^p$. Many recursions and other representat …
- 171
1
vote
Lower bound for constrained ordered partitions (i.e., compositions)?
For my answer, I assume that compositions are on non-negative numbers (allowing only positive numbers does not change my statements, qualitatively).
First, observe that $p(N,m,n)=\binom{m}{n}_{N+1}$, …
- 171