Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry in maximal $(s-1,s+1)$ cores   We explain a "curious symmetry" for maximal $(s-1,s+1)$-core partitions first
observed by T. Amdeberhan and E. Leven. Specifically, using the $s$-abacus, we
show such partitions have empty $s$-core and that their $s$-quotient is
comprised of 2-cores. This imposes strong conditions on the partition
structure, and implies both the Amdeberhan-Leven result and additional
symmetry. We also find a more general family that exhibits these symmetries.

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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: cond-mat