CHAIN DECOMPOSITION THEOREMS FOR ORDERED SETS (AND OTHER MUSINGS)

JONATHAN DAVID FARLEY

Abstract. A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can be partitioned into chains in a “strong” way, is proved. The result is motivated by a conjecture of Graham’s concerning probability correlation inequalities for linear extensions of finite posets.