turkmath.org

Consider n molecules lined up in a row. From among the n - k + 1 nearest neighbor k-tuples, we select one uniformly randomly and bond the k molecules together. Then from the remaining nearest neighbor k-tuples, we select one uniformly randomly and bond the k molecules together. We continue this way until there are no nearest-neighbor k-tuples left. Let M(n;k) denote the random variable that counts the number of bonded molecules, and let E[M(n;k)] denote the the expected value of M(n;k). I will present the proof of the following result by R. G. Pinsky [1]: E(M(n;k))/n converges to an explicit constant p(k) as n tends to infinity. The result for k = 2 goes back to an article in 1939 by Paul Flory, 1974 Nobel Laureate in Chemistry. Some open problems will be discussed at the end of the talk.