Geodesic
A new encoding of permutations by Laguerre histories
Sherry H.F. Yan1 ; Hao Zhou ; Zhicong Lin2
1Zhejiang Normal University
2Jimei University
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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We construct a bijection from permutations to some weighted Motzkin paths known as Laguerre histories. As one application of our bijection, a neat $q$-$\gamma$-positivity expansion of the $(\mathrm{inv},\mathrm{exc})$-$q$-Eulerian polynomials is obtained.
DOI : 10.37236/8661
Classification : 05A05, 05A19, 11B68
Mots-clés : weighted Motzkin paths, (\(\mathrm{inv}\), \(\mathrm{exc}\))-\(q\)-Eulerian polynomials

Sherry H.F. Yan  1   ; Hao Zhou    ; Zhicong Lin  2

1 Zhejiang Normal University
2 Jimei University 
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     author = {Sherry H.F. Yan and Hao Zhou and Zhicong Lin},
     title = {A new encoding of permutations by {Laguerre} histories},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {3},
     doi = {10.37236/8661},
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Sherry H.F. Yan; Hao Zhou; Zhicong Lin. A new encoding of permutations by Laguerre histories. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8661

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