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arXiv · 2211.06871

A bijection for length-$5$ patterns in permutations

Joanna N. Chen·Zhicong Lin
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Abstract

A bijection between $(31245,32145,31254,32154)$-avoiding permutations and $(31425,32415,31524,32514)$-avoiding permutations is constructed, which preserves five classical set-valued statistics. Combining with two codings of permutations due respectively to Baril--Vajnovszki and Martinez--Savage proves an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.

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Joanna N. Chen, Zhicong Lin. 2022-12-22. A bijection for length-$5$ patterns in permutations. https://arxiv.org/abs/2211.06871

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