Journal of Integer Sequences, Vol. 25 (2022), Article 22.5.4

An Exact Enumeration of the Unlabeled Disconnected Posets

Salah Uddin Mohammad, Md. Shah Noor, and Md. Rashed Talukder
Department of Mathematics
Shahjalal University of Science and Technology


We give an exact enumeration of the unlabeled disconnected posets according to the number of connected components of the posets. This result establishes that the enumeration of unlabeled posets belonging to a class that is closed under the direct sum depends mainly on the enumeration of unlabeled connected posets contained in the class. We also give an algorithm to determine the parameters involved in the enumeration formula, and finally, find the number of unlabeled disconnected posets with a certain number of elements. We show that the enumeration algorithm runs in polynomial time.

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(Concerned with sequences A000112 A202182 A263864 A349367 A349401 A350783.)

Received February 08 2022; revised version received June 5 2022. Published in Journal of Integer Sequences, June 16 2022.

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