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Counting self-dual interval orders

Abstract : In this paper, we first derive an explicit formula for the generating function that counts unlabeled interval orders (a.k.a. (2+2)-free posets) with respect to several natural statistics, including their size, magnitude, and the number of minimal and maximal elements. In the second part of the paper, we derive a generating function for the number of self-dual unlabeled interval orders, with respect to the same statistics. Our method is based on a bijective correspondence between interval orders and upper-triangular matrices in which each row and column has a positive entry.
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Vít Jelínek. Counting self-dual interval orders. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.539-550. ⟨hal-01215055⟩

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