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Baxter permutations are a class of permutations which are in bijection with aclass of floorplans that arise in chip design called mosaic floorplans. Westudy a subclass of mosaic floorplans called $HFO_k$ defined from mosaicfloorplans by placing certain geometric restrictions. This naturally leads tostudying a subclass of Baxter permutations. This subclass of Baxterpermutations are characterized by pattern avoidance. We establish a bijection,between the subclass of floorplans we study and a subclass of Baxterpermutations, based on the analogy between decomposition of a floorplan intosmaller blocks and block decomposition of permutations. Apart from thecharacterization, we also answer combinatorial questions on these classes. Wegive an algebraic generating function (but without a closed form solution) forthe number of permutations, an exponential lower bound on growth rate, and alinear time algorithm for deciding membership in each subclass. Based on therecurrence relation describing the class, we also give a polynomial timealgorithm for enumeration. We finally prove that Baxter permutations are closedunder inverse based on an argument inspired from the geometry of thecorresponding mosaic floorplans. This proof also establishes that the subclassof Baxter permutations we study are also closed under inverse. Characterizingpermutations instead of the corresponding floorplans can be helpful inreasoning about the solution space and in designing efficient algorithms forfloorplanning.

Sub-families of Baxter Permutations Based on Pattern Avoidance