Decomposing labeled interval orders as pairs of permutations

Anders Claesson; Stuart A. Hannah

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arXiv · 1405.2441

Decomposing labeled interval orders as pairs of permutations

Anders Claesson·Stuart A. Hannah

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Abstract

We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices fixed under this involution are in bijection with labeled interval orders and that they decompose to a pair consisting of a permutation and an inversion table. To fully classify such pairs, results pertaining to the enumeration of permutations having a given set of ascent bottoms are given. This allows for a new formula for the number of labeled interval orders.

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Anders Claesson, Stuart A. Hannah. 2014-05-10. Decomposing labeled interval orders as pairs of permutations. https://arxiv.org/abs/1405.2441

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