Semiorders and Riordan Numbers
Barry Balof and Jacob Menashe
Department of Mathematics
Walla Walla, WA 99362
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 nth 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.
Full version: pdf,
(Concerned with sequences
Received February 14 2007;
revised version received July 18 2007.
Published in Journal of Integer Sequences, July 23 2007.
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