On two--block--factor sequences and one--dependence

The distributions of two--block--factors $(f (\eta_{i},\eta_{i+1}); \, i \geq 1)$ arising from i.i.d. sequences $(\eta_{i}; \, i \geq 1)$ are observed to coincide with the distributions of the superdiagonals $(\zeta_{i,i+1}; \, i \geq 1)$ of jointly exchangeable and dissociated arrays $(\zeta_{i,j}; \, i, j \geq 1)$. An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.