Enumeration of Corners in Symmetric Tree-like Tableaux

Laborde-Zubieta conjectured a formula to enumerate corners in symmetric tree-like tableaux. By exploring the relationship among symmetric tree-like tableaux, symmetric alternative tableaux, permutation tableaux of type $B$ and signed permutations, we reduce L.-Z.'s conjecture to counting the number of signed descents and ascents in signed permutation, and thus confirm this conjecture. Moreover, we give a conjectural $x$-analogue of this enumeration.