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Chain Decomposition Theorems for Ordered Sets (and Other Musings)

Jonathan David Farley
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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.

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Jonathan David Farley. 1997-07-16. Chain Decomposition Theorems for Ordered Sets (and Other Musings). https://arxiv.org/abs/math/9707220

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