The poset of proper divisibility
Loading...
Access rights
openAccess
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2017
Major/Subject
Mcode
Degree programme
Language
en
Pages
17
2093-2109
2093-2109
Series
SIAM Journal on Discrete Mathematics, Volume 31, issue 3
Abstract
We study the partially ordered set P(a1, ... , an) of all multidegrees (b1, ... , bn) of monomials xb1 1 ... xbn n, which properly divide xa1 1 ... xan n . We prove that the order complex Δ(P(a1, ... , an)) of P(a1, ... an) is (nonpure) shellable by showing that the order dual of P(a1, ... , an) is CL-shellable. Along the way, we exhibit the poset P(4, 4) as a new example of a poset with CL-shellable order dual that is not CL-shellable itself. For n = 2, we provide the rank of all homology groups of the order complex δ(P(a1, a2)). Furthermore, we give a succinct formula for the Euler characteristic of δ(P(a1, a2)).Description
Keywords
CL-shellability, Euler characteristic, Posets, Proper division, Simplicial homology
Other note
Citation
Bolognini , D , Macchia , A , Ventura , E & Welker , V 2017 , ' The poset of proper divisibility ' , SIAM Journal on Discrete Mathematics , vol. 31 , no. 3 , pp. 2093-2109 . https://doi.org/10.1137/15M1049142