Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Naruse hook formula for linear extensions of mobile posets   Linear extensions of posets are important objects in enumerative and
algebraic combinatorics that are difficult to count in general. Families of
posets like Young diagrams of straight shapes and $d$-complete posets have
hook-length product formulas to count linear extensions, whereas families like
Young diagrams of skew shapes have determinant or positive sum formulas like
the Naruse hook-length formula from 2014. In 2020, Garver et. al. gave
determinant formulas to count linear extensions of a family of posets called
mobile posets that refine $d$-complete posets and border strip skew shapes. We
give a Naruse type hook-length formula to count linear extensions of such
posets by proving a major index $q$-analogue. We also a inversion index
$q$-analogue of the Naruse formula for mobile tree posets.

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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph