  Tree-like tableaux are objects in bijection with alternative or permutation
tableaux. They have been the subject of a fruitful combinatorial study for the
past few years. In the present work, we define and study a new subclass of
tree-like tableaux enumerated by Baxter numbers. We exhibit simple bijective
links between these objects and three other combinatorial classes: (packed or
mosaic) floorplans, twisted Baxter permutations and triples of non-intersecting
lattice paths. From several (and unrelated) works, these last objects are
already known to be enumerated by Baxter numbers, and our main contribution is
to provide a unifying approach to bijections between Baxter objects, where
Baxter tree-like tableaux play the key role. We moreover get new enumerative
results about alternating twisted Baxter permutations. Finally, we define a new
subfamily of floorplans, which we call alternating floorplans, and we enumerate
these combinatorial objects.
