Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Refinement of the Murnaghan-Nakayama Rule by Descents for Border Strip
  Tableaux   Lusztig's fake degree is the generating polynomial for the major index of
standard Young tableaux of a given shape. Results of Springer and James &
Kerber imply that, mysteriously, its evaluation at a $k$-th primitive root of
unity yields the number of border strip tableaux with all strips of size $k$,
up to sign. This is essentially the special case of the Murnaghan-Nakayama rule
for evaluating an irreducible character of the symmetric group at a rectangular
partition.
  We refine this result to standard Young tableaux and border strip tableaux
with a given number of descents. To do so, we introduce a new statistic for
border strip tableaux, extending the classical definition of descents in
standard Young tableaux. Curiously, it turns out that our new statistic is very
closely related to a descent set for tuples of standard Young tableaux
appearing in the quasisymmetric expansion of LLT polynomials given by Haglund,
Haiman and Loehr.

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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: eess