Moment Calculus on Ramsey Graph

When I did my thesis defense presentation eleven years ago, I chose to present the subject of Ramsey theory from the moment calculus perspective. I don't think I did too well there (although I passed). Time has passed and this is the chance to redeem myself. Here we relate Ramsey numbers, $R(k,k)$, with the method of moment calculus by checking the distribution of numbers of monochromatic complete subgraph of $k$ vertices in the random graphs. We also review Delaporte distribution's connection that was mentioned in the paper by Robertson, Cipolli and Dascalu.