Journal of Integer Sequences, Vol. 24 (2021), Article 21.4.7

On the Number of Antichains and Antichain Covers of Labeled Sets

Paweł Marcin Kozyra
Institute of Mathematics
Pedagogical University of Krakow
Podchorążych 2
30-084 Krakow


We present a formula for the number of antichains consisting of m subsets of a labeled n-element set, as well as a formula for the number of all m-antichain covers of a labeled n-element set. We also give a simple formula for the number of antichain covers that are composed of sets of the same cardinality.

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(Concerned with sequences A000372 A000392 A006126 A016269 A047707 A051112 A056046 A056047.)

Received September 1 2020; revised versions received February 17 2021; April 16 2021. Published in Journal of Integer Sequences, April 17 2021.

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