Cyclic Permutations of Sequences and Uniform Partitions
Cyclic Permutations of Sequences and Uniform Partitions
Let $\vec{r}=(r_i)_{i=1}^n$ be a sequence of real numbers of length $n$ with sum $s$. Let $s_0=0$ and $s_i=r_1+\ldots +r_i$ for every $i\in\{1,2,\ldots,n\}$. Fluctuation theory is the name given to that part of probability theory which deals with the fluctuations of the partial sums $s_i$. Define $p(\vec{r})$ to be the number …