Decomposing labeled interval orders as pairs of permutations
Combinatorics
2014-10-22 v2
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.
Cite
@article{arxiv.1405.2441,
title = {Decomposing labeled interval orders as pairs of permutations},
author = {Anders Claesson and Stuart A. Hannah},
journal= {arXiv preprint arXiv:1405.2441},
year = {2014}
}