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.Comment: 26 pages, 11 figures. This is the final version for publicatio
