In any discrete setting, one of the most natural questions to ask is “How many of these objects are there?” The automorphism problem (Open Question 2.14) and Dedekind’s problem (Open Question 2.30) are questions like that. A counting question can be motivated by pure curiosity or, as the Kelly Lemma (see Proposition 1.40) in reconstruction shows, it can be a useful lemma for proving further results. The two most natural counting questions for ordered sets are still unanswered and it appears that both are quite hard.
KeywordsGrade Level Formal Power Series Grade Function Rank Function Linear Extension
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