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.
@article{10_37236_4360,
author = {Anders Claesson and Stuart A. Hannah},
title = {Decomposing labeled interval orders as pairs of permutations},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {4},
doi = {10.37236/4360},
zbl = {1298.05023},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4360/}
}
TY - JOUR
AU - Anders Claesson
AU - Stuart A. Hannah
TI - Decomposing labeled interval orders as pairs of permutations
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4360/
DO - 10.37236/4360
ID - 10_37236_4360
ER -
%0 Journal Article
%A Anders Claesson
%A Stuart A. Hannah
%T Decomposing labeled interval orders as pairs of permutations
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4360/
%R 10.37236/4360
%F 10_37236_4360
Anders Claesson; Stuart A. Hannah. Decomposing labeled interval orders as pairs of permutations. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4360
