Bootstrap percolation, the Schro¨der numbers, and the N-kings problem
SIAM Journal on Discrete Mathematics
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
Proceedings of the 7th conference on Formal power series and algebraic combinatorics
Pattern matching for permutations
Information Processing Letters
Corner block list: an effective and efficient topological representation of non-slicing floorplan
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Floorplan representations: Complexity and connections
ACM Transactions on Design Automation of Electronic Systems (TODAES)
On the number of rectangular partitions
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Space-planning: placement of modules with controlled empty area by single-sequence
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
VLSI module placement based on rectangle-packing by the sequence-pair
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Twin binary sequences: a nonredundant representation for general nonslicing floorplan
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Bounds on the number of slicing, mosaic, and general floorplans
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Optimizing regular edge labelings
GD'10 Proceedings of the 18th international conference on Graph drawing
The Hopf algebra of diagonal rectangulations
Journal of Combinatorial Theory Series A
European Journal of Combinatorics
Optimal binary representation of mosaic floorplans and baxter permutations
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Bijective Counting of Involutive Baxter Permutations
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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A floorplan represents the relative relations between modules on an integrated circuit. Floorplans are commonly classified as slicing, mosaic, or general. Separable and Baxter permutations are classes of permutations that can be defined in terms of forbidden subsequences. It is known that the number of slicing floorplans equals the number of separable permutations and that the number of mosaic floorplans equals the number of Baxter permutations [B. Yao, H. Chen, C.K. Cheng, R.L. Graham, Floorplan representations: complexity and connections, ACM Trans. Design Automation Electron. Systems 8(1) (2003) 55-80]. We present a simple and efficient bijection between Baxter permutations and mosaic floorplans with applications to integrated circuits design. Moreover, this bijection has two additional merits: (1) It also maps between separable permutations and slicing floorplans; and (2) it suggests enumerations of mosaic floorplans according to various structural parameters.