Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A minimaj-preserving crystal on ordered multiset partitions   We provide a crystal structure on the set of ordered multiset partitions,
which recently arose in the pursuit of the Delta Conjecture. This conjecture
was stated by Haglund, Remmel and Wilson as a generalization of the Shuffle
Conjecture. Various statistics on ordered multiset partitions arise in the
combinatorial analysis of the Delta Conjecture, one of them being the minimaj
statistic, which is a variant of the major index statistic on words. Our
crystal has the property that the minimaj statistic is constant on connected
components of the crystal. In particular, this yields another proof of the
Schur positivity of the graded Frobenius series of the generalization $R_{n,k}$
due to Haglund, Rhoades and Shimozono of the coinvariant algebra $R_n$. The
crystal structure also enables us to demonstrate the equidistributivity of the
minimaj statistic with the major index statistic on ordered multiset
partitions.

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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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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: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an