Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A bijective proof of Macdonald's reduced word formula   We give a bijective proof of Macdonald's reduced word identity using pipe
dreams and Little's bumping algorithm. This proof extends to a principal
specialization due to Fomin and Stanley. Such a proof has been sought for over
20 years. Our bijective tools also allow us to solve a problem posed by Fomin
and Kirillov from 1997 using work of Wachs, Lenart, Serrano and Stump. These
results extend earlier work by the third author on a Markov process for reduced
words of the longest permutation.

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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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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-ex
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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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: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin