## Semiorders and Riordan numbers

### Summary

Summary: In this paper, we define a class of semiorders (or unit interval orders) that arose in the context of polyhedral combinatorics. In the first section of the paper, we will present a pure counting argument equating the number of these interesting (connected and irredundant) semiorders on $n+1$ elements with the $n$th Riordan number. In the second section, we will make explicit the relationship between the interesting semiorders and a special class of Motzkin paths, namely, those Motzkin paths without horizontal steps of height 0, which are known to be counted by the Riordan numbers.

05A15, 06A07

### Keywords/Phrases

riordan numbers, interval orders, semiorders, lattice paths