17 May
2005
17 May
'05
12:07 a.m.
The second paragraph below (using the separators to count the ways that I increments can be binned into k-1 bins) is flawed -- it overcounts the ways by I'm not sure what factor at this hour. Oh, well. --Dan << Think of the I increments as dots in a row. The number of ways they can be distributed into k-1 bins is the same as the way we can separate the I dots using k-2 vertical lines each before, between, or after the I dots. (Two or more separators are allowed to have 0 dots between them.) The number of ways to arrange the separators, and equally to interpolate a nondecreasing sequence between X1 and Xk, is thus (I+1)^(k-2).