Geodesic
A bijection between evil-avoiding and rectangular permutations
Katherine Tung1
1Harvard University
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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Evil-avoiding permutations, introduced by Kim and Williams in 2022, arise in the study of the inhomogeneous totally asymmetric simple exclusion process. Rectangular permutations, introduced by Chirivì, Fang, and Fourier in 2021, arise in the study of Schubert varieties and Demazure modules. Taking a suggestion of Kim and Williams, we supply an explicit bijection between evil-avoiding and rectangular permutations in $S_n$ that preserves the number of recoils. We encode these classes of permutations as regular languages and construct a length-preserving bijection between words in these regular languages. We extend the bijection to another Wilf-equivalent class of permutations, namely the $1$-almost-increasing permutations, and exhibit a bijection between rectangular permutations and walks of length $2n-2$ in a path of seven vertices starting and ending at the middle vertex.
DOI : 10.37236/11841
Classification : 05A05, 05A15, 68Q45
Mots-clés : inhomogeneous totally asymmetric simple exclusion process, Wilf-equivalent class of permutations

Katherine Tung  1

1 Harvard University 
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Katherine Tung. A bijection between evil-avoiding and rectangular permutations. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11841

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