Combinatorials

Our first goal was to calculate the exact distribution for the number of unbalanced triangles, under the permutation model. This proved to be too hard, and so we decided to look at an approximation of that model, the sampling with replacement model. But after stumbling upon the work of Hoeffding – in particular (Hoeffding ⊕1951Hoeffding, Wassily. 1951. “A Combinatorial Central Limit Theorem.” The Annals of Mathematical Statistics 22 (4): 558–66.) – we instead change our tactic to looking at the asymptotic distribution under the permutation model.

It turns out that it’s actually really easy to calculate moments.