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2. Stability of Stretched Root Systems, Root Posets and Shards

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   Dana, Will ( July 2021 , The Electronic Journal of Combinatorics)

   Inspired by the infinite families of finite and affine root systems, we define a "stretching" operation on general crystallographic root systems which, on the level of Coxeter diagrams, replaces a vertex with a path of unlabeled edges. We embed a root system into its stretched versions using a similar operation on individual roots. For a fixed root, we describe the long-term behavior of two associated structures as we lengthen the stretched path: the downset in the root poset and Reading's arrangement of shards. We show that both eventually admit a uniform description, and deduce enumerative consequences: the size of the downset is eventually a polynomial, and the number of shards grows exponentially. 

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4. Ant invasion is associated with lower root density and different root distribution of a foundational savanna tree species

   https://doi.org/10.1007/s10530-023-03008-4  

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