Séminaire Lotharingien de Combinatoire, 80B.56 (2018), 12 pp.

Henri Mühle and Vivien Ripoll

Connectivity Properties of Factorization Posets in Generated Groups

Abstract. 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.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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