Joanna N. Chen, Zhicong Lin
Published 2022-11-13Version 1
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.
Comments: 27 pages, 6 figures
Counting (3+1) - Avoiding permutations
The distribution of consecutive patterns of length 3 in $3\textrm{-}1\textrm{-}2$-avoiding permutations
A bijection between triangulations and $312$-avoiding permutations
![QR code for arXiv:2211.06871 [math.CO]](http://oss.arxitics.com/images/favicon.svg)