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Applied Combinatorics

Section 6.9 Discussion

Over coffee, Bob said that he really liked this chapter. “This material was full of cases of very concrete procedures for doing useful things. I like that.” Yolanda offered a somewhat different perspective “On the other hand, this last procedure only seems to work with interval orders and we still don’t have a clue as to how to find the width of a poset in the general case. This might be very difficult—like the graph coloring problems discussed in the last chapter.” Dave weighed in with “Somehow I think there’s going to be a fairly efficient process that works for all posets. We may not have all the tools yet, but let’s wait a bit.”
Not much was said for a while and after a pause, Carlos ventured that there were probably a lot of combinatorial problems for posets that had analogous versions for graphs and in those cases, the poset version would be a bit more complicated, sometime a little bit and sometimes a very big bit. Zori was quiet but she was thinking. These poset structures might even be useful, as she could imagine many settings in which a linear order was impossible or impractical. Maybe there were ways here to earn a few dollars.