Counting Self-Dual Interval Orders

Details Counting Self-Dual Interval Orders Counting Self-Dual Interval Orders

2011-06-11

arxiv.org/abs/1106.2261v1

Journal of Combinatorial Theory, Series A, 119(3), 599-614 (2012)

Mathematics

Combinatorics

20 pages

Scientific paper

10.1016/j.jcta.2011.11.010

In this paper, we present a new method to derive formulas for the generating functions of interval orders, counted with respect to their size, magnitude, and number of minimal and maximal elements. Our method allows us not only to generalize previous results on refined enumeration of general interval orders, but also to enumerate self-dual interval orders with respect to analogous statistics. Using the newly derived generating function formulas, we are able to prove a bijective relationship between self-dual interval orders and upper-triangular matrices with no zero rows. Previously, a similar bijective relationship has been established between general interval orders and upper-triangular matrices with no zero rows and columns.

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