Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dyck tilings, increasing trees, descents, and inversions   Cover-inclusive Dyck tilings are tilings of skew Young diagrams with ribbon
tiles shaped like Dyck paths, in which tiles are no larger than the tiles they
cover. These tilings arise in the study of certain statistical physics models
and also Kazhdan--Lusztig polynomials. We give two bijections between
cover-inclusive Dyck tilings and linear extensions of tree posets. The first
bijection maps the statistic (area + tiles)/2 to inversions of the linear
extension, and the second bijection maps the "discrepancy" between the upper
and lower boundary of the tiling to descents of the linear extension.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: physics