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Separable d-Permutations and Guillotine Partitions
Andrei Asinowski1 and Toufik Mansour2
1Caesarea Rothschild Institute, University of Haifa, Haifa 31905, Israel
2Department of Mathematics, University of Haifa, Haifa 31905, Israel
Annals of Combinatorics 14 (1) pp.17-43 Springer, 2010
AMS Subject Classification: 05A05, 05A15, 05C30
We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2d-1-dimensional box is constructed. We also study enumerating problems related to guillotine partitions under certain restrictions revealing connections to other combinatorial structures. This allows us to obtain several results on patterns in permutations.
Keywords: d-permutations, separable permutations, patterns in permutations, guillotine partitions, binary trees, Schr¨oder paths


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