The reason I've asked this question is that I want to use LAD LASSO regression $\min_{\beta} \left| \mathbb{y} - \mathbb{X} \boldsymbol{\beta}\right|_1 + \lambda \left|\boldsymbol{\beta}\right|_1$ and be able to have constraints on coefficients. I've asked it here: stats.stackexchange.com/questions/76538/…

Andrew, thank you for this proof. It might be silly question, but could you please clarify how do you link real uniformly distributed numbers with permutations of integer numbers. Do you do mapping, link each selected real number with its rank in a generated sequence?

Alexey, could you please comment what do you mean by cycle?

Thank you! This what I suspected. Indeed I've tried to calculate exact distributions for small cases, up to N=10 and tried to find dependencies. It looks like some kind of fluctuations around binomial coefficients. For instance, in case of N=5 the distribution is (2,4,14,32,18,28,14,8). I just thought, could it be reduced to a problem of partitioning of integer number N... P.S. Did you obtain your graph from random sampling from permutations?

Greg, by computing recursively do you mean we assume some generation function?

That's right. The consecutive elements means elements with indexes i and i+1, i+1 and i+2 and so on, where i runs from 1 to N. Therefore, elements with indexes 1 and N are not consecutive.