There are two natural simplicial complexes associated to the noncrossing partition lattice: the order complex of the full lattice and the order complex of the lattice with its bounding elements removed. The latter is a complex that we call the noncrossing partition link because it is the link of an edge in the former. The first author and his coauthors conjectured that various collections of simplices of the noncrossing partition link (determined by the undesired parking spaces in the corresponding parking functions) form contractible subcomplexes. In this article we prove their conjecture by combining the fact that the star of a simplex in a flag complex is contractible with the second author's theory of noncrossing hypertrees.
@article{10_37236_7212,
author = {Michael Dougherty and Jon McCammond},
title = {Undesired parking spaces and contractible pieces of the noncrossing partition link},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/7212},
zbl = {1386.05011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7212/}
}
TY - JOUR
AU - Michael Dougherty
AU - Jon McCammond
TI - Undesired parking spaces and contractible pieces of the noncrossing partition link
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/7212/
DO - 10.37236/7212
ID - 10_37236_7212
ER -
%0 Journal Article
%A Michael Dougherty
%A Jon McCammond
%T Undesired parking spaces and contractible pieces of the noncrossing partition link
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/7212/
%R 10.37236/7212
%F 10_37236_7212
Michael Dougherty; Jon McCammond. Undesired parking spaces and contractible pieces of the noncrossing partition link. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7212
