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Ordered Sets pp 333-356 | Cite as

Enumeration of Ordered Sets

  • Bernd Schröder
Chapter
  • 1.1k Downloads

Abstract

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.

Keywords

Grade Level Formal Power Series Grade Function Rank Function Linear Extension 
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.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Bernd Schröder
    • 1
  1. 1.Department of MathematicsUniversity of Southern MississippiHattiesburgUSA

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