The Impact of the Chain Decomposition Theorem on Classical Combinatorics
Kenneth P. Bogart, Curtis Greene, Joseph P. S. Kung · Birkhäuser Boston eBooks · 1990
Dilworth’s chain decomposition has become such a standard concept for specialists in ordered sets that at the NATO Advanced Study Institute on Ordered Sets held in Banff in 1981 participants would use the phrase “Dilworthtype theorem” when they meant “minimax theorem” or when they meant “partition theorem.” Harper and Rota, in their foundational survey of matching theory [30], describe a number of equivalent matching theorems which can be stated as minimax theorems and are all derivable from each other. Among these, they choose Dilworth’s theorem as “perhaps the most elegant.” Mirsky and Perfect regard Dilworth’s theorem as perhaps “the most fundamental among the finite results” of this type in matching theory [46]. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.