Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transitive powers of Young-Jucys-Murphy elements are central   Although powers of the Young-Jucys-Murphya elements X_i = (1 i) + ... +(i-1
i), i = 1, ..., n, in the symmetric group S_n acting on {1, ...,n} do not lie
in the centre of the group algebra of S_n, we show that transitive powers,
namely the sum of the contributions from elements that act transitively on {1,
>...,n}, are central. We determine the coefficients, which we call star
factorization numbers, that occur in the resolution of transitive powers with
respect to the class basis of the centre of S_n, and show that they have a
polynomiality property. These centrality and polynomiality properties have
seemingly unrelated consequences. First, they answer a question raised by Pak
about reduced decompositions; second, they explain and extend the beautiful
symmetry result discovered by Irving and Rattan; and thirdly, we relate the
polynomiality to an existing polynomiality result for a class of double Hurwitz
numbers associated with branched covers of the sphere, which therefore suggests
that there may be an ELSV-type formula associated with the star factorization
numbers.

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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat