Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of stretched root systems, root posets, and shards   Inspired by the infinite families of finite and affine root systems, we
consider 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 study the growth of
two associated structures as we lengthen the stretched path: the downset in the
root poset (in the sense of Bj\"orner and Brenti [3]) and the arrangement of
shards, introduced by Nathan Reading. 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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The categories of this paper are: hep-ex
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th