Geodesic
Enumeration of Corners in Tree-like Tableaux
Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3 Cet article a éte moissonné depuis la source Episciences

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In this paper, we confirm conjectures of Laborde-Zubieta on the enumeration of corners in tree-like tableaux and in symmetric tree-like tableaux. In the process, we also enumerate corners in (type $B$) permutation tableaux and (symmetric) alternative tableaux. The proof is based on Corteel and Nadeau's bijection between permutation tableaux and permutations. It allows us to interpret the number of corners as a statistic over permutations that is easier to count. The type $B$ case uses the bijection of Corteel and Kim between type $B$ permutation tableaux and signed permutations. Moreover, we give a bijection between corners and runs of size 1 in permutations, which gives an alternative proof of the enumeration of corners. Finally, we introduce conjectural polynomial analogues of these enumerations, and explain the implications on the PASEP. 
@article{DMTCS_2016_18_3_a16,
     author = {Gao, Alice L. L. and Gao, Emily X. L. and Laborde-Zubieta, Patxi and Sun, Brian Y.},
     title = {Enumeration of {Corners} in {Tree-like} {Tableaux}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2015-2016},
     volume = {18},
     number = {3},
     doi = {10.46298/dmtcs.1408},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1408/}
}
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Gao, Alice L. L.; Gao, Emily X. L.; Laborde-Zubieta, Patxi; Sun, Brian Y. Enumeration of Corners in Tree-like Tableaux. Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3. doi: 10.46298/dmtcs.1408

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