  Baxter permutations are a class of permutations which are in bijection with a
class of floorplans that arise in chip design called mosaic floorplans. We
study a subclass of mosaic floorplans called $HFO_k$ defined from mosaic
floorplans by placing certain geometric restrictions. This naturally leads to
studying a subclass of Baxter permutations. This subclass of Baxter
permutations are characterized by pattern avoidance. We establish a bijection,
between the subclass of floorplans we study and a subclass of Baxter
permutations, based on the analogy between decomposition of a floorplan into
smaller blocks and block decomposition of permutations. Apart from the
characterization, we also answer combinatorial questions on these classes. We
give an algebraic generating function (but without a closed form solution) for
the number of permutations, an exponential lower bound on growth rate, and a
linear time algorithm for deciding membership in each subclass. Based on the
recurrence relation describing the class, we also give a polynomial time
algorithm for enumeration. We finally prove that Baxter permutations are closed
under inverse based on an argument inspired from the geometry of the
corresponding mosaic floorplans. This proof also establishes that the subclass
of Baxter permutations we study are also closed under inverse. Characterizing
permutations instead of the corresponding floorplans can be helpful in
reasoning about the solution space and in designing efficient algorithms for
floorplanning.
