Decomposing labeled interval orders as pairs of permutations

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Claesson, Anders and Hannah, Stuart A. (2014) Decomposing labeled interval orders as pairs of permutations. The Electronic Journal of Combinatorics, 21 (4). P4.16. ISSN 1077-8926 (https://doi.org/10.37236/4360)

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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.

ORCID iDs

Claesson, Anders ORCID logoORCID: https://orcid.org/0000-0001-5797-8673 and Hannah, Stuart A.;
CORE (COnnecting REpositories)