Geodesic
Connectivity Properties of Factorization Posets in Generated Groups
Séminaire lotharingien de combinatoire, 80B (2018)

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We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of elements in generated groups. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework to study these connectivity properties in a uniform way. Our main tool is a certain total order of the generators that is compatible with the chosen element. 

@article{SLC_2018_80B_a55,
     author = {Henri M\"uhle and Vivien Ripoll},
     title = {Connectivity {Properties} of {Factorization} {Posets} in {Generated} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a55/}
}
TY  - JOUR
AU  - Henri Mühle
AU  - Vivien Ripoll
TI  - Connectivity Properties of Factorization Posets in Generated Groups
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a55/
ID  - SLC_2018_80B_a55
ER  - 
%0 Journal Article
%A Henri Mühle
%A Vivien Ripoll
%T Connectivity Properties of Factorization Posets in Generated Groups
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a55/
%F SLC_2018_80B_a55
Henri Mühle; Vivien Ripoll. Connectivity Properties of Factorization Posets in Generated Groups. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a55/