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arXiv · 2105.08762

Diameters of graphs of reduced words and rank-two root subsystems

Christian Gaetz·Yibo Gao
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Abstract

We study the diameter of the graph $G(w)$ of reduced words of an element $w$ in a Coxeter group $W$ whose edges correspond to applications of the Coxeter relations. We resolve conjectures of Reiner--Roichman and Dahlberg--Kim by proving a tight lower bound on this diameter when $W=S_n$ is the symmetric group and by characterizing the equality cases. We also give partial results in other classical types which illustrate the limits of current techniques.

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Christian Gaetz, Yibo Gao. 2021-05-18. Diameters of graphs of reduced words and rank-two root subsystems. https://doi.org/10.1090/proc%2F15912

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