On the Number of Posets

TL;DR

This paper investigates the combinatorial properties of unlabeled posets, revealing that the differences in their counts stabilize as the number of points increases, and introduces related new sequences.

Contribution

It provides new insights into the enumeration of posets, including the stabilization of differences and the extension of OEIS sequences using combinatorial and graph theory methods.

Findings

Differences in the number of posets become stationary for large point counts.

Introduces a new sequence A376894 based on these differences.

Extends existing OEIS sequences using combinatorial arguments.

Abstract

This paper presents combinatorial facts dealing with the number of unlabeled partially ordered sets (posets) refined by the number of arcs in the Hasse diagram (sequence A342447 in OEIS). The main result is that the differences with respect to the number of points in this sequence become stationary if the number of points is sufficiently high. These differences are proposed as the new sequence A376894. In addition, the underlying combinatorial and graph theoretical arguments were used to extend some further OEIS sequences.